What I found to be the easiest method to beat the Stage 2 boss: Whole holding forward: jump and attack, then mash attack until you land. Repeat.

Faster route for Stage 2: I haven't found a consistent route for the ghost, so this is a very risky way to save 2-3 seconds.

I landed on something in midair: Maybe wall jumps are possible? There probably won't be much of a use for wall jumps in a run but I thought it was interesting.

Nudua found out how to make the patterns of the bosses predictable by starting the game within a tight window. The info on how is found here: http://nudua.com/files/avenging-spirit-rng-manip.zip

Clip1) Consistent boss2 quick kill

Clip2) Alternative boss3 quick kill, bit faster than going behind him right away. Requires set pattern from correct starting frame

Clip3) Consistent boss5 quick kill, nothing new. Requires set pattern from correct starting frame

Clip4) Manipulation of fly enemy for damage boost. Full jump couple frames after gaining control and he will land toward you for boost.

Clip5) Alternative stage6 up to laser guy capture. ~0.8 seconds faster than old route, but has similar ghost RNG than stage2 that can kill the run.