I had problems with this 2. I just finished the miss yesterday. I first tried it at lvl 43 with an undergeared Skadge. I did not succeed. Through other quests/HR/WZ I lvl-ed to 44 and also geared Skadge with some better armer and impants/earpiece etc. I just barly made it. Btw, i'm dual-specced 'run-and-gun'.
What i did is the following:
Just start with the normal rotation. The problem is those 4 droids who come in later in the fight. When the droids show up, put everything in, relics, shield, hydraulic etc. Skadge should attack those droids, I stay'd on Barrows. You can, however, walk away a bit to avoid being hit. Barrows will not follow you. When you almost on 0-health you should walk away, pop in a med-pack, let skadge attack Barrows after he defeated all the droids. When Skadge almost gets killed, return, stun an finish Barrows.
Hopefully it works for you!