Leviathan is one of the toughest opponents to beat in X Men Origins Wolverine. In fact, that is the level from where the game warms up. The best way to beat Leviathan is to get onto its shoulder from behind and repeatedly attack him. During this time he will slowly raise his hand to hurt your player, make sure that you use Space to jump just before he attacks you. Do not Lunge straight at Leviathan, as he will smack you out with his hands.
Instead, wait for it to attack you, then roll around to move behind it and Lunge at it. This will put you in a position to hack at its one crack in the armor. Repeat this until until you’ve taken away its health. take some time to recover by dodging around until you regain strength, to avoid running out of power. It took me 9 tries to beat him but that helped me beat other tough players with relative ease due to the practice I got from Leviathan. Below is a video to further help you see this process of beating this rock monster.