Here's the trick to beating Shadow Destroyer at the end of Resistance.
When Shadow Destroyer spawns, several small Void Riflts also appear, and Shadow Destroyer will naturally approach one of them. This rift sustains his hyper-regenerating damage shield - destroy it, and the shield will go down and Shadow Destroyer will be stunned for about eight seconds, giving you some time to pound on him.
Don't approach the big rift in the center of the battlefield. Getting in the pink effect will cause steady damage-over-time and slowly drag you to the center. If you touch the center itself, you've got a second or two to escape before you're instantly defeated. The big rift is simply an environment hazard; at no point do you need to interact with it or even step in it during the fight.
Dr. Destroyer will happily tank everything that Shadow Destroyer puts out, if you let him, and will also tank the lesser Trey Kings monsters too. If you can get them all hung up on Dr. Destroyer, then you can focus solely on Shadow Destroyer and his rifts. Dr. Destroyer is pretty much impossible for Shadow Destroyer and his monstrosities to kill, even when he calls out Endbringer (see below).
When Shadow Destroyer gets low, he will retreat to the Qliphothic Rift and a cutscene will play, where he will summon Endbringer. Endbringer is fantastically powerful, but Dr. Destroyer can still tank everything that Endbringer can dish out; let him do so and beat down on Endbringer mercilessly. Periodically, Shadow Destroyer will emerge from the Qliphothic Rift to harass you while you're fighting Endbringer. When he does, drop everything and maul Shadow Destroyer until his shield drops (Unlike with the void rifts earlier, it takes very little effort at all), and then he'll retreat back to the Rift. Once he retreats, return to beating Endbringer down.
When Endbringer is defeated, you've won. A cutscene will play, Dr. Destroyer will gloat, and you get your loot.
NOTE: I'm not sure if it's Normal difficulty or Soloing that activates it, but you may have the assistance of a couple Resistance members during the final fight against Shadow Destroyer. They won't actively fight, but they will produce Green and Blue boosts for you to pick up. If the Resistance members are there, make use of them.