Cloud has all of his Limit Breaks in Tactics, plus Cherry Blossom, so yes, Climhazzard is his and with good reason. I believe it does the amount of damage an enemy has taken to them, so if they've lost 350 HP it does 350 damage. Either that or it does the amount of damage Cloud himself has taken. I think that one's Blade Beam though.

Now, for the next inevitable FFX question... "Dude, where the hell is Aerith?"
(SPOILER)Dead, where she belongs. Though she does make a cameo in Tactics, or at least it's a girl thats supposed to be just like her, which is why Cloud comes to save her after he's been transported to the Ivalice.