This is a solution for those of you trying to take out these dragons on ultimate vault hunter mode in a group.

You should obviously be level 61. You will definitely want to have a siren that can use res. You'll want to use guns that can pump out massive damage such as the sand hawk and the unkempt harold. Use bees with maybe someone using an evolution for survivability. Bring eredium for ammo.

There are 4 different dragons you're going to be taking out. The way this fight works is the dragons will fly around and shoot you with their different elements and which ever dragon you hit first in the air will land. If you have a siren, they can just phaselock the dragon that you want to target. It is important to recall any turrets you put out while a dragon was on the ground and try not to use deathtrap until there are only 2 dragons left. As the battle progresses, the dragons will also increase in level, making them harder to kill. There are 2 ammo shrines that you can use to fill your ammo, although it does cost 2 eredium each time.

The first one you should take down is the lightning dragon. He can heal the other dragons so he needs to go first. Open the battle by shooting at him when all the dragons are hovering around. If it starts to fly around again, make sure to only shoot at the lightning one so that it lands.

Once the lightning dragon is dead, next to go is the fire dragon. This dragon is the hardest to kill. When he first lands DO NOT shoot him. You'll see a spiral flame coming up from his body. This means he cannot be hit and all bullets will be reflected! The floor will also start to light on fire. You want to avoid the platforms that are starting to glow because they will deal massive damage when the fire starts. After the spiral flame is gone, you can unload on the dragon and do as much damage to it as you can before it takes off. Now just make it land and repeat this until it is dead.

After you've killed the lightning and fire dragons, its probably best to take out the corrosive dragon, but at this point it doesn't matter what order you go in because they are both fairly weak. This is when you can start using deathtrap and leaving turrets out.

For the corrosive dragon, there isn't much to say other than it summons mobs so if you go down, you'll have a way to get back up.

The slag dragon is by far the easiest to kill. My buds and I noticed that sometimes the slag dragon likes to land in the middle of the fight for no apparent reason.
Overall just try to survive reviving people as soon as they go down.