Lame boss. You should prepare for this boss before reaching him. You want a gun that is accurate which means it will hit from a distance. Boss has 3 phases
1st phase: He starts out just machine gunning you. You need to watch out for explosives on the platform you are standing on. Use the turrets on each of the 4 corners to add some extra DPS and distract the boss while you blast him
2nd phase: he will add a rail gun to his routine. Just make sure you are moving in any direction that isn't in line with the rail gun shot.
3rd phase: He now adds rockets to the mix but not many. Same thing as phase 2 but with 2 times the adrenaline in your system.
Video clip of my speed run (Note I am very strong level 65 damage and level 50 health) Video is 1 minute long:
Turrets are key here. If you managed to kill the first boss on this run then you should have got a key from him that you can use on this level, after the boss dies, to get a legendary weapon like a flame thrower or battle rifle. It looks like a weapon container only it is orange instead of blue