The easiest way to earn this trophy is to play as Lilith. You will want to utilize the ledge glitch (see video below) to defeat Crawmerax. If you are skilled enough with a rocket launcher, proceed to use any class and take out Crawmerax's weak spot in his back using the method in the video. Credit goes to wavern's channel.
When using Lilith, instead of using a rocket launcher, you can enter the field of play where Crawmerax and his minions will attack you. Lure them to either side of the huge rock formations on either side of to map. Once you've done this, activate her action skill and run over to the opposite rock formation where Crawmerax is. Allow the action skill to recharge and then proceed to pop out and shoot Crawmerax in the back until he charges at you. Rinse and repeat. See video below. Credit goes to Matt Pascual.
Happy Hunting :)