He’ll always reset to full HP if he steps past one of the gates. I believe the reason this is the case is probably just a fail-safe just in case somebody tries some obscure exploit like luring him out of the arena to safespot him. This is just my own speculation.
If he’s on the wall with you but off to the side, do not try to move in his red circle until during an attack. Lupicus, along with all other mobs in this game, will only attempt to correct their target being out of their line of sight in between attacks. The reason that a person is capable of preventing his necrid trap (bubble) attack and the rapid fire one at all is because when he’s against the wall, he isn’t able to travel in the direction that he attempts to, due to the wall blocking his movement. These two skills of his require a target to be a certain distance from him in order to use, similarly to how for example you won’t be able to place a banner as far away from you as you would be able to shoot something with a longbow (poor example I know).
In other words, it’s flawed AI. What would ideally be the case is that when unable to move in any other direction anymore, attempt to move in another direction instead.
This is why it’s ambiguous whether or not pushing him against the wall is considered an exploit/cheating, as it’s not using unintended mechanics (like leaping onto terrain/safespotting) to succeed in the fight but more or less just knowing the limitations of mob AI in the game and taking advantage of/abusing it. No different than LOSing/stacking tbh.
Long answer, but hopefully you’ll better understand it now.
when trying to solo lupi I pulled him to the wall he then moved eventually to the gates that open by my mistake. On phase two after awhile he just walked off back to where he always stands then his hp went back to full and took up aggro again. I gave up came back and got him to phase 3 10% of his health was left he did the same thing is there something im doing wrong?
ill keep him away from that gate next time.