If you do the gate thing, be very careful how far back you go - you can inadvertently reset the dragon’s health. (Extremely frustrating when that happens) I’ve done the fight on UVHM successfully without a fire immunity shield. When I did it with Sal, I was using a booster shield and mostly staying on the platform immediately in front of the gate rather than behind it.
My biggest problem on that fight has always been the baby dragons that get dropped onto the bridge. Tesla grenades help immensely with those, as they can take a bunch of health off before the small dragons get through to you. A decent RL helps if they still manage to put you into FFYL.
For the big dragon, a good pair of SMGs can do the job (slag + shock seems to be a good combo). I’ve always found the DPUH awkward for that fight due to the slow projectile speed.