So two things about the Endbringer weakness thing.
1) WoG, every Shard has the ability to cause flight. It's incredibly simple for them to do. Most just don't bother because of some alien space whale logic. Thus, every Endbringer should be capable of flight, but only the Simurgh bothers. This could be a form of self-telekinesis or extremely rapid teleportation that appears as fluid movement or a mobile gravity well or- well anything really, but they're capable of it, just as they're capable of far more than ever demonstrated in the series. Remember, the Endbringers are sandbagging hard.
2) not WoG AFAIK but it's implied or hypothesized in-story that Endbringers layer their flesh across multiple dimensions, keeping the property of durability but massively reducing their effective weight. This effect becomes more pronounced as you approach the core, while outer layers of flesh only function as a pretty durable crystalline material. Further in, the overlap crosses over the Schwarzchild radius (if that's how you spell it) by a massive margin. It's pure Shard magic that this doesn't result in a black hole. The effect can be thought of as similar to Chevalier's power, where he layers multiple objects into a single instance and can select which properties of the constituent objects to manifest, including effective mass and volume.
3) none of an Endbringer's flesh matters but the core. If trapped, they can remove the trapped area. Certain parahuman effects just don't work as they approach the core- namely, Chevalier's combined weapon actually shattered into its constituent objects upon contact with Behemoth's core. Their core has defenses other than just being very massive and durable. The fact that their mass is separated over multiple dimensions means that just hitting the core isn't enough- even if you do manage to damage this instance of the core, there's a thousand thousand other dimensions with a layered copy of the core. Effectively, only Sting and Scion can actually meaningfully damage a core.
Now, as for what actually could Mission Kill an Endbringer... there are a few ways. Such as having Labyrinth and Scrub punch them into a different dimension, or having String Theory use a mass driver to punt them out of orbit, where they'll just stop working. Haywire could probably do so as well, but his status is never elaborated (that I know of) so who knows where he is or if he's alive.
Any way of disabling an Endbringer other than "put it somewhere else" would be... difficult. They tried for decades with more capes than are ever named and failed. Endbringers count against any applicable Manton Limits- they're either organic or inorganic, whichever counts in their favor. That invalidates most powers that could otherwise be useful. That leaves temporary half-measures like Clockblocker spending his entire life pausing Leviathan until another Endbringer decides to kill him, or actually giving the Endbringers what they want and fighting a losing fight.
Edit: did I say two? More than two. I fail math forever.