The final boss of the game, not as daunting as it seems.
The first thing you want to do is take out the purple sac things on its tentacles. They fire out poisonous dart-like arrows which can arc over the pillars you hide behind, so taking them out is a must, preferably with a scoped SMG.
Once the initial two tentacles have been destroyed, wait for the Destroyer to open its mouth so you can shoot at its tongue. Don't bother with its giant eye, the amount of time lining up a shot to hit it gives him enough time to hit you and the tongue remains a critical hit spot.
After dealing sufficient damage to its tongue, the Destroyer will wrap a tentacle around a couple of pillars either side of the arena. Before you do anything else, take out the 4 new tentacles it has spawned to avoid the poisonous arrow attack. They drain your shield and health like no tomorrow.
After the 4 tentacles have been destroyed, if you are a Berserker, activate your Beserk attck and keep punching the tentacles wrapped around the pillars until it dies. If you are one of the other 3 classes, I still recommend using your special attack, but you must focus on finding scattered ammo, normally near the New-U station.
As previously mentioned by other solutions, if you are close to dying, JUMP OFF THE EDGE OF THE ARENA. You will return to full health whereas the Destroyer will be on the same amount.
As it is the final boss of the game, it will obviously not go down in one or two hits. This is an endurance battle, but as lon as you keep your wits about you, it won't pose too much of a threat.