I haven't seen anybody figure this out, but you can actually do a "challenge run" of Unlock Everything by jumping over a bunch of unlocks -- most notably, the health and buster upgrades. This of course makes the game much more difficult, as one hit from anything kills you and your rate of firing is much slower.

Here's my run of the game, collecting as few upgrades as possible:

https://www.youtube.com/watch?v=MOKBzgJpw58

Interestingly enough, the boss (which most people struggle with) is actually the easiest part of this run. Some of the earlier cannon rooms are a little difficult to get through and will require some more practice to get through without getting hit.

If I have the time I'll make some quality of life improvements to make speedruns and such easier to do (skipping cutscene dialogue, etc).