There are several spots in this level where you will have a good chance of dying due to getting spammed by laser fire. It's best to do this one with one of the ghost characters. Ignore everything except getting to the end of the level and be careful of falling into the pit around the Millennium Falcon at the end.
Also, be sure that no extras are turned on! You might want to start your "no death" runs from a fresh restart of the game. All extras are turned off by default when you launch the game.