Superman is a good example, but EDL took it.
To be fair to the question, there often isn't a very good answer. That's a reason DC's universe hasn't done as well in the movie business; most of the characters of the DC universe are simply too powerful in their comic form for us to feel any dramatic tension about any situation this superhero faces, and powering them down creates an implausible character. The exception is Batman, a very human character with a very gritty, real backstory, that stands up to the kind of cinematic drama modern audiences expect. The Marvel universe has gotten away with more powering-down of heroes from godlike comic form, both because there tend to be more of them (so no one character has to carry a whole team), and because the general moviegoing public is less familiar with Marvel comics. That can't be plausibly done with Superman. We know Superman. He's one of the most recognizable superheroes in pop culture. We know his powers, the speed, the strength, the laser vision, the hurricane breath. We can't limit those powers and realistically expect an audience to play along. A movie, or even a scene, in which he's anything less than "super", no matter how little chance an ordinary human in his place would have, breaks the WSD.
That right there is pretty much the best way to create dramatic suspense around an omnipotent hero character. The hero will likely be just fine no matter what, so it's hard to feel nervous about them. Instead, make us like a squishy little human, then put them in the middle of the battle royale. All of a sudden the hero's fighting with one arm tied behind their back, limited in what powers they can use that won't fry the human, where they're allowed to be and for how long without the villain getting too good a chance at crushing the human, and what counts as "defeating" the villain, given that the human might just have emotional ties to the villain. This creates more unknowns than a straight toe-to-toe fight, especially if you've done a good job setting up the hero to be as powerful in the audience's mind as you want them to be.
The only other plausible way to create dramatic suspense is a moral dilemma, where there is no "good" outcome, there are only differently bad outcomes. "Can't save 'em both" situations, where making the decision or taking the time/action to save one kills the other, are examples. While quite effective if played straight, forcing the perfect hero to deal with the personal consequences of an imperfect world, many writers (and audiences) want to have their cake and eat it too, so this trope is too often subverted with "well actually, I can". That typically boils down to "I win because you're an idiot who left this obvious loophole in your dastardly plan", or "I win because I'm so powerful I can break the laws of the universe as everyone understood them until just now". Both are cliche'd beyond most usefulness, except where it's so cliche it's what your audience expects (e.g. Bond movies and their ridiculously complicated deathtraps, or superhero origin stories where the audience expects to have the physics of the real world turned upside-down as this hero discovers their true power)