Imposing Challenger

Q. You move Imposing Challenger in against Kha'zix Mutating Horror. Can you move it to the other Battlefield before it gains its +2 Might bonus from defending?

Yes. The move trigger is resolved before the staged combat begins. Kha'iz is not yet designated as a defender. in this situation, this also means that because Kha'zix was removed from the battlefield before the combat, there is no longer a combat staged at the Battlefield and a non-combat Showdown will take place. Any "win a combat" trigger you may have would not trigger.

455 A combat occurs when a Cleanup occurs, there are no items on the Chain, there is a staged Combat at a battlefield, and no Showdown or Combat is ongoing at any other Battlefield.