What are tomb runs?

what are those?

tomb "runs" are the battles on your way to the HoH.

in order to make it to the Hall of Heroes yo must go through a coupel rounds of prelimanary battles in order to earn your way there.

Except that it varies incredibly based on when your fight happens to end relative to when the hall battle is decided. Have been in round after round of tombs without getting there, taking out team after team, and others get there after 2 wins. The randomness is a killer, which is why you see people doing the "Dance into the HoH" that one team did.

I can only go to HoH after i beat last missoin?

You just have to get to the Dragon's Lair