Ok I'm currently watching it right now and up until a bit after Corridor 1, things seems great. But here are the things I've noticed:
In the area where you receive the upgrade for the first rapid fire, on your way back up, you avoid a butterfly monster to avoid damage. You should've just taken the hit because it's slightly slower to move diagnolly than in a straight direction. I know you're trying to avoid getting hit, but in instances like these where it saves time, just take the hit and move on.
Also, in the miniboss fight with the crab monster right above that rapid fire power-up I just mentioned, after you killed him and received the item he dropped, you didn't move straight back for the exit, instead, doing some weird loop. Why?
Also, another instance of taking damage when you should've occurred in the room above the room with the giant W in the main area. You killed two monsters with your bat to avoid damage. Again, you should just take the hit.
In Area 2, coordinates x5 and y15, fighting against the blue crab boss, it kinda looks like you didn't begin firing at him as soon as possible. Of course I could be wrong, but from playing the game for so many years, it seems like you could've started damaging him a few frames earlier. Is this just how it looks, or did you actually start damaging him as soon as he's available for taking damage?
In x2 y17 of area 2, you shoot a spider. Again, take the hit.
In x2 y15 (I believe), you did the same with another butterfly monster.
The blue miniboss fought in x1 y14 was fought beautifully!
In x2 y14, take the hit.
The blue lander upgrade you picked up right after that probably could've been picked up faster had you taken the hit...again.
In x3 y16, take the hit.
Corridor 2 was awesome, and I love how you killed him JUST as you went down to 0 health! Now THAT is entertainment.
Corridor 3 was also great. But would it be faster to also die after leaving there. From the top of my head, I know the room with the blue lander in which you spawn in isn't too far away to walk to, but it might be slightly faster to die after the third boss than walk all the way back. This should be tested.
Anyways, so far, I think you're doing great, but I think in all instances in which you would save time by taking damage, go for it. Now, I listed a lot of instances in which you should take damage. I don't know how much health you'd have left after all that, but if by some chance you have none and THEN you come across a room where you have to kill an enemy so as to not die, THEN don't take damage. I'm really not trying to be picky about that because I know you're adamant on taking little damage, but I'm fairly certain the finished product would be rejected otherwise.
Keep up the great work. :)