I don't see why Darksied couldn't beat him the same way the Surfer did:
The Surfer dashes out and flies past the speed of light in the other direction, and goes back in time to before the nuclear explosion responsible for the Overlord's mutation and prevents the accident from happening. Thus the Overlord was never a mutant, and the whole ordeal was undone. The Surfer then goes back to his own time and is once more trapped within Earth's barrier.
Regardless, the omega effect should be able to take him out. Unless Overlord borrows Superman's jobber aura before the fight starts. 😬