This will probably go like Aquaman vs Hercules (Except Ulik isn't completely out of it and hallucinating). Arthur is facing someone with a noticeably strength and durability edge, but Aquaman is more agile and intelligent.
If he tries to fight Ulik punch for punch, he goes down, but give him his trident, and he can wear him down and shit for the win possibly. But if Ulik has his pounders, Aquaman can't afford to get hit even once.