I don't even know why I picked up Trevor mode. I had originally picked this game back up because Zewing wanted some info on how to run Hector mode. After looking over my notes, I realized that I had never actually rerouted the game like I had planned (equipment and IDs). So started doing that.
One day I just decided to play around with Trevor mode for fun. See if I even remembered how to play him. Did a full playthrough. Then I decided to see how well I could do for any%. On my first run with minimal routing and planning, with multiple deaths, I managed a 1:37:xx by the in game clock, which beat the previous segmented record by 6 minutes. It all kind of snowballed from there. (Note that I had never actually watched Aquatiger's run before that first attempt, even though it had been sitting on my hard drive for about 5.5 years...)

Trevor has numerous combos he can do with his whip, but there's only 2 that are really of any use in a speedrun: Windmill and Torpedo.
-Windmill deals (((ATK - DEF) x 0.6) - 1) damage for each hit but the last one, which deals full damage. This can hit up to 7 times I think.
-Torpedo is the fastest form of movement Trevor has. Over the course of a really long hallway (tested on the ramparts in Abandoned Castle), Quick Stepping takes about 24 seconds vs. Torpedo which takes 20 seconds. Overall it saves about 0.5 seconds per Torpedo compared to Quick Stepping. The Quick Step in between most Torpedoes doesn't cost any time at all, and has the added benefit of more control over what direction I'm heading in.

Out of all the subweapons, Knife is the most useful, followed by Stopwatch.
Well, Knife Crush is useful anyway - it deals 10 damage per hit for the duration of the attack. This damage does not increase over the course of the game, and any enemy that has a defense greater than 0 severely affects it's usefulness.
Stopwatch allows me to keep enemies at bay for a length of time...it's usually saved for fast moving/hard hitting/flying enemies, for obvious reasons. Stopwatch Crush uses 10 extra hearts to freeze time twice as long (5 seconds vs. 10 seconds). Correct usage of this isn't always to use the Crush since I don't always need the full 10 seconds to do what I need to do, and doors won't unlock until after time starts moving again. In addition heart management comes into play, since this is by far the most costly subweapon.
Cross Crush (Grand Cross) gets a little use breaking open a wall in Eneomaos Machine Tower, and is extremely useful against Death.
Holy Water Crush is useful in a couple select places.
Axe is never used in any%.

The run itself:

Abandoned Castle:
Went really well except when the knives decided to target the wrong ghost in the basement. Very minor time loss, though.
Grabbing the Attack Up here costs about 20-25 seconds, which is more than made up for throughout the rest of the run.

Baljhet Mountains:
Very short area since Trevor can skip the latter two-thirds of it. The lone battle room went perfectly.
The Attack Up here takes about 50 seconds to grab - this was the most controversial one to pick up. After making an estimate for how much time it saves on bosses, I was still about 16 seconds shy of it actually saving time. After some deliberation, I figured that it has to save at least some time in normal battle rooms, and even if it ends up costing time it can't be more than a handful of seconds. At best it may even save a few seconds. Either way, it makes some battle rooms and bosses easier due to the increased attack.

Mortvia Aqueduct:
Mostly went well, except the room right before the Circle Tip, where a Merman had way more HP than it should have had, and the Skeleton Wolf room where I was having trouble hitting them.
Grabbing the Attack Up here only costs about 20ish seconds, which is of the same usefulness as the one in Abandoned Castle.

Skeleton Diver:
This was a really lucky fight outside of him perfect guarding my initial assault after he jumped on the platform. I use the Knife Crush to keep the Diver stunlocked so I can beat on the Fish when it flops onto the platform. When the Diver is mounted on the Fish, it's possible to hit both of them with one attack with proper aiming.

Forest of Jigramunt:
There's actually very little fighting in this area, until near the end.
The trigger for opening the door in the room with all the Bone Soldiers is a bit unusual: The Dark Warlock and the 5 Bone Soldiers nearest the way I came in have to die to trigger the Thief spawning. The other Bone Soldiers don't matter at all. I have no idea why they set this room up like this.
There's an HP MAX UP in the 2nd room of the caves, but it's a bit of a detour, and while it's good for anyone just starting out with running this category, it's unnecessary for those with experience.
Unfortunately I didn't reach the save point with 150+ HP, which meant I needed to take the save there. Minotaurus' hits all do around 50 damage, and I want as much of a cushion as I can get.

Minotaurus:
This definitely wasn't my greatest fight...it started with some bad luck with how he turned - he pushed Trevor off to the side, which made some of my initial whips miss. Those missed attacks wouldn't have been a big deal except my strat requires constant damage. Minotaurus only flinches when he takes enough damage/hits, and with my current damage output, he won't flinch properly if I miss any shots. The knives are only used to add hits. Without them it's impossible to keep him stunned.
When Minotaurus drops below 25% HP he'll change his pattern, and add jumping and spinning to his arsenal. It's beyond possible to perfect guard the jumps, but missing one will send me flying, and do quite a bit of damage, so I played it safe. The Holy Water works best once he's in this phase since staggering him becomes exponentially more difficult.

Cordova Town:
The first third of this area has no battle rooms. I have no idea why.
In the Assassin Zombie room, one of them managed to escape before I could get to it. I was able to drag it up the hill a bit, so minimal time loss.
In the Skeleton Rider room, one of the first 2 mounts started running around and it took me a few tries to nail it. I need to remember to attack the same one my Knives are going after.
The rest of the battle rooms went quite well.
I hit the save point before Isaac because I always want full HP going in here. Isaac has ended more than a few runs.

Isaac:
Isaac himself went pretty well comparatively. I want to keep my Knives on his ID since that's the only way to keep it off of me. If I had the Ice Whip I could freeze it, but any% skips that. Even though you'd think keeping the Knives on Isaac would be a good idea (since he has a defense value of 0, which allows the knives to do full damage), it's actually better to keep them on his ID since Isaac can randomly block/dodge any attack. Having the knives on him causes this to happen a LOT, which means I whip him less as a result. Note that the hesitation when his ID gets ready to explode is due to how much damage it does - 100+ depending on how long it's been charging for. At full charge it's over 150, which I can't afford to take.

Eneomaos Machine Tower:
The biggest factor in this area is that I'm at the mercy of Heart drops. I use an alternate route to get to Saint Germain, one which lacks a save point. If my heart count is too low when I reach him, it's pretty much game over. The route I use takes the way that Hector is intended to come down after the fight. Since Trevor doesn't use IDs, they installed teleporters to allow Trevor to pass those areas. They, however, didn't remember to take them out on the way up. Going up and coming back down this way saves about 1:45 over the intended way, and has the same number of battle rooms.
All of the battle rooms went really well here, except the one with 2 Flame Demons...the auto-targeting decided that the one I had already killed was a better target than the one that was still alive.
I picked up the Thunder Whip since Saint Germain is weak to it, and there's also a couple other places it's useful later on. The Grand Cross is the fastest way to destroy that wall.

Saint Germain:
Other than the slightly rocky start, Saint Germain went beautifully. I was able to catch him after he teleported out of my combo and prevent him from attacking me. I generally don't use the Windmill attack in this fight since Saint Germain has a certain number of attacks he'll take before teleporting (it varies, but it's usually 6-10 from what I've seen). Since normal attacks hit for full damage, it increases how much damage he takes in between each teleport.
Also, The (almost) sole reason I was picking up the Heart Max Ups was for this fight. Being too low on hearts is a run killer.
Unlike Hector, Trevor has no quick way to get out of here, so I have to backtrack to the warp room. Going the same way I came up is faster than taking the elevator down, even though neither way has any battle rooms.
Before anyone asks, you don't have to activate the Baljhet warp room...it's always activated just so you'll always have somewhere to warp to.

Trevor Doppelganger:
This guy has ended a few runs, though he's not that dangerous. Outside of not using Holy Water when he still had his shield up, this fight went pretty well.
When his shield is up, he cannot be made to flinch at all. Once he suffers enough damage the shield will drop.
The best way to deal with him once his shield is down is to try and either perfect guard his combos, then counterattack, or to dodge out of the way and counter, knocking him out of his attacks. I have to be mindful of when he attacks, though, and get out of the way in time since he does deal a fair bit of damage. Defeating him before he activates his shield for a second time means the fight was a fast one.

Infinite Corridor:
The Thunder Whip is very useful against the Final Guards since they are weak to it. In addition, Bone Soldiers and Spirits take the same number of hits to kill with the Thunder Whip as they do with the Circle Tip, so there's no point switching until after all the Final Guards at the beginning are done with.
I made a slight mistake in the room with all the Ectoplasms and the two Wights. I should have only used normal Stopwatch instead of Stopwatch Crush. It only wasted a few seconds though.
Speaking of Wights, they are easily the most irritating enemy in this entire area. They can fly through walls, and sit around in places I can't reach. I was just lucky that both rooms with them went as well as they did.
Overall, this area went much better than normal, and was the biggest time improvement over my last run.

Dullahan:
This fight is very RNG based. There's one attack he does where he points his sword straight down and charges for a few moments. During the charge up, he takes double damage...sadly he didn't use this at all this time around (unlike last time where he used it twice). He did jump a lot though, which allows me to get full combos off on him. I also use the Knife Crush here since Dullahan has a defense value of 0.
Once again, Trevor has no quick way to get out of here (unlike Hector who is automatically teleported to the Mortvia Aqueduct warp room). The backtrack isn't too long, thankfully.

Dracula's Castle:
The one thing about this area that required some somewhat extensive testing was whether or not the Square Tip was worth it. It adds +10 Attack Power over the Circle Tip, which is actually pretty huge for the final boss gauntlet. However, it takes around 1:25 to go get,
And doesn't save anywhere near that on the final four bosses. In addition there's only 8 battle rooms between the Square Tip and the end, which means it's an overall net loss of time.
I will say that I got relatively good luck in most of the battle rooms. The rooms with Flame/Frost Demons are probably the most RNG heavy, even though I use Stopwatch Crush to keep them in place. If they don't all spawn near each other, it's pretty much guaranteed that one or more of them will get away when it wears off. The Frost Demon room upstairs went perfectly. The Flame Demon room almost had one get away, but I was able to get it before it took off. The Frost Demon room downstairs had an unlucky spawn, and there was no easy way to hit all of them. I got extremely lucky that I was able to take out those last two before they moved.
I have to be relatively mindful of my Heart count here...the save rooms have quite a bit of distance between them, and this area is fairly heart intensive, mostly thanks to the Stopwatch. I get a bit more breathing room once I'm out of the basement, thankfully.

Isaac:
The biggest thing here is that Isaac must never be allowed to do anything. Once he drops below 80% HP, he'll summon an ID (Crimson). Not only does he waste time with the summon, but he's also completely invincible while this ID is out. When he drops below 60% he'll recall the Crimson if it's out and summon an Iytei. He takes minimal damage while this one's out - not enough to be worth attacking him. Below 40% he summons a Rasetz. He takes full damage while this one's out, but has increased knockback resistance.
The Knife Crush works wonders for keeping him stunlocked. I have a setup that allows me to keep track of exactly when I need to use another Knife Crush: I do 3 full combos, then whip twice. Knife Crush should end during the last hit, allowing me to use it again before Isaac has a chance to move.

Death:
Outside of breaking the wall for the Thunder Whip, this is the only other place you'll see me use the Cross. It's the perfect way to dodge his scythe swings and continue dealing damage at the same time. It also manipulates his fire scythe into a pattern that won't hit me after I tank the initial hit. It can also manipulate the tiny sickles into flying up, which allows me to keep attacking (he didn't use this attack this time though).
The optimal pattern here is when Death just keeps swinging his scythe at me, which is almost exactly what he did minus the one fire scythe.
When Death drops below 50% HP he'll always do a Fireball next. Without more attack power, it's not possible to kill him before I take a hit. I do try to perfect guard the initial hit, but the camera angle is really awkward for doing that, so it's pretty rare that I time it correctly.
I screwed up one of the perfect guards and ended up taking a second hit for it. If I had messed up 2 hits sooner, I would have died from it, so I was extremely fortunate in that regard. In addition, if my assault after the fireball ended hadn't killed him, I would have also died since there wouldn't have been enough time to dodge his next attack.

Dracula:
Dracula has high defense, but low HP. If he teleports to the back of the room and does the lasers, Grand Cross works wonders. Holy Water also works well when he uses spikes.
When he did his first attack, I dodged the wrong way and took a hit for it. Other than that this fight went well. I need to come out of this fight with high HP for Drac 2.

Final Dracula:
Even though I've practiced the shit out of this guy and have done quite a number of attempts, Final Dracula still scares the shit out of me. He hits like a truck, cannot be stunned, and has a random amount of windup before all of his punches, making it almost impossible to time perfect guards.
Coming into this fight with high HP is a must - it's almost inevitable that I'll take damage here. As the fight progresses, I start taking it more and more cautiously. I've lost a number of good runs to this guy, which is always a heartbreaker.
Overall though, this was a good fight. Even though I took a number of hits, I didn't get hit by any of the big damage ones. The overhead smash is the one I really have to play it safe around, since it can easily double hit. I got really lucky with the timing of my dodges, since dodging too early can cause me to still take the hit.
The only reason I use Knife Crush here is for some extra damage. No other subweapon is worth using since I'm too weak for them to have any oomph. Grand Cross was a consideration, but it doesn't elevate me high enough to avoid most of his attacks.

Closing thoughts:
Is this time improvable? Probably. My execution was good, but not perfect. Overall the luck was good though, which would make getting a run better than this difficult. For now I'm going to leave the time at this, and maybe come back to this run another time.

Thanks:
-SDA staff for hosting my runs
-Aquatiger for doing the original run. While I changed quite a few of the strats, I still learned a fair bit from his run
-My stream regulars who sat through me grinding attempts