How do you die?
Is it due to the turrets or something else?
Make sure all the systems that you can shut down/overload like the containment system are down too.
You're not doign anything wrong. Theres' nothing that you need to do except destroy the turrets. The the door then opens normally. You don't even have to kill the droids (I somethimes leave as many as possible to get the experience for them.