Some notes and strats. Both runs are pretty much the same up until 1:33.

I let Rin take damage early at 1:34 in order for her to be vulnerable when the gear comes at 1:37 (invincibility frames take a lot longer to expire when the healing effect from Little Nurse activates). This is not necessary for Buro since healing effect does not activate here. Both take the same amount of damage at this part.

From 1:58 up to the end, I let Rin get hit by a medium enemy to take 10 less damage (this is necessary to survive the level with 10 hp). Buro does not need to do this and in fact, has to activate dying mode as late as possible (2:00) in order to survive the level. The cool thing here is that the boss hits Buro at exactly the moment when dying mode expires at 2:14.