Wicked K is unlocked after beating the Crucible in one sitting - waves 1-100. You _cannot_ die/leave without completing all of them in one go. See the following:
Solution for Is There Anyone Else? In Darksiders IIfor some help with that. You need to be at least level 25 to unlock waves 75-100 so this will have to be done on New Game+ (as there is a level cap of 22 on your first playthrough).
Once you do that, the Arena will open up and you need to climb up to Wicked K (for which you need the Deathgrip, so make sure you have at least grabbed it from the Foundry). You are permitted to leave after beating wave 100 to restock if you wish (just come back, talk to the Arena Master and choose to start on Wicked K from his wave selection list - the middle will rise again).
Climb up and beat him. He is not particularly difficult if you stay away from him (he has some close up moves that hurt). I was able to do it on level 25 with 5 maxed Teleport Slashes and stacked crit chance (on Easy). For some specific info check out the end of the following guide:
http://segmentnext.com/2012/08/17/darksiders-2-crucible-mode...Once you beat him you get a scene that makes you think you just took some acid and this nice achievement.