There is nothing hard in this mission, it's just very time consuming. As the others are saying, you really need to be a higher, at least level 25 or more to beat the dragons. What I did is stop worrying about the quest, beat the game 2 times (as leveling up really requires to play on True Vault Hunter mode above level 20-22) and I've just aimed nothing but reach level 35 in the first place:
As the others say, Murderlin is really your best way to leveling up after you beat the main story line. In the meantime in every 2-3 levels I went to Mines of Avarice and used the Lootapult to get better gear (as obtaining Skeleton Keys for the Golden Chest is kind of an impossible mission these days...)
I also visited the The Seraph Vendor to buy a relatively powerful Assault rifle. (The way as Is ee it is always a Torque weapon, but it has homing missiles so I highly recommend to use these during your walkthrough) Once you reached Level 35 and has a relevant gear to your level, you don't even need to prioratize between targets, just focus on one drgaon at the time and shoot it dead. If you turn on Easy mode, dying is basicly not an option.