I did this last night, got 0/5 stars but I did it, lol... in the worst way. I was Snow, as a Sentinal, had Hope as a Medic, and Fang as a Commando, Fang did ALL the damage, I just stood there with Snow and took the majority of damage, while Hope kept everyone alive with his heals. Only problem was, when we'd get those status effects, sometimes Hope would make removing those a higher priority then actually healing us, so this failed me a few times. I really don't think I should have been able to beat this giant Cactus, he is a pain, I just got lucky, maybe you could too. If not, just do some other missions and collect lots of CP, then go back and fight him.
Well, wait, you did finish the game once already right? because if you just got to Chapter 11 and started doing the side missions, some will be impossible for you... because your Crystarium isn't fully expanded, you won't be able to be as strong as you can get, making most of the side missions not doable. I've already finished the game and came back to this place, so that might be why you're having such a hard time getting your characters HP up.
when you beat the game you unlock the last part of the crsytarium and alot of health upgrades are in it, when you beat it your able to teleport to gran pulse to grind some more yes lots of grinding ive been grindin for quite a bit and most my guys got around 15k hp