If you're not after really fast times on the Nikimaru Counter, you can try to get a few shots in right after it fires, and then focus more on getting items from the Butes. Otherwise, you could stay under it as much as possible, using the Booster 2 to dash between the Deleets when necessary.
For Heavy Press, I say use your level 1 Spur. Constantly shoot upwards at him, and then when he starts charging his shot, move to the side and shoot sideways at the angel thingies (pick up hearts when they drop them). Oh yeah, you'll need to be constantly jumping over the rolling eyeballs. One time I did it only losing 2 health in total but I haven't been able to repeat that since. I can't imagine doing it with only 3HP.