Soloing that is tough because it's a guild quest, and the game assumes you're playing with four players. That's probably why you're having the most trouble, I think they take 70% of the damage you normally dish out?
In any case, what poison weapon are you using? Generally I'm able to solo Kush with my Chameleos weapons, but I'm not sure if you've gotten to play against that dude yet. The IG in particular lets you keep hitting him while he's in the air, and you can ground him with enough hits. Alternatively, aim to cut the tail. If the wiki is to be believed, that will weaken the barrier.