Stupid Boss concept I've committed myself to

Title basically. I've begun planning a campaign with the goal of destroying the egg of a ludicrously powerful, CR 90, 3.5e time dragon while it weaponizes the butterfly effect against you.

I need a final boss. Now, under no circumstances can they beat this thing in a fair fight. It was never made to be fought. Buuuuut, it could make a pretty good gimmick boss fight!

The dragon can barley be touched by most attacks, and can't be affected by lingering spells. So I imagine, in between regular attacks (this thing is perma-hasted too), it goes back in time, butterflies, and changes the world in the present to try and gain the advantage. But each arena change has a way to damage it integrated. 

Changes it to a dark fantasy Conan-like world? Oh hello castle siege with convenient ballistas.

Gothic horror dark crystal deal? Unfinished magic ritual. Nice to see you 

Scifi future? Turns out this plot of land is perfect for a mech docking station

Cyberpunk world? Hiii godlike ai who isn't cool with this giant dragon destroying its city!

The win condition isn't killing it, that's definitely off the table, it's breaking its egg and maybe wounding it

If anyone has other suggestions for ways to damage this thing, feel free to tell me