This will be the first quest you complete in the game. After choosing a character and losing in, follow Claptrap around the area. Claptrap will eventually get abducted by Shiv and you will face off against him. After fighting Shiv and freeing Claptrap, Lillith will drop in. You will then face off against another wave of enemies.
Afterwards, go and talk to Lillith and the quest will complete and the trophy will pop.