Well if I remember right.. here are some tips(may not be perfect). -----spoilers on how I fight the last boss below (highlight if hard to read)
The pre final form or right after you are rewarded the 9 lives. drool will show up in three robot parts for around 30 seconds, stay on the lower two/thirds of the screen and do a clockwise circle to avoid the lightning and missiles, shoot the missiles and use your backfire to destroy the missiles the best you can. you will likely die at least once here.
Final form hug the left wall and avoid projectiles by moving up and down, charge for a few seconds and shoot charge shot.. repeat
Again missiles are the worst thing he shoots, do small loops around the missiles when he shoots these
When you die and come back invincible you can swoop in for a few free backfires by hovering on the boss but its a little risky because as you are getting back to the left side projectiles may get you.