i have beaten the league quite a few times while having him in my party. And now i have begun to fight a lot at the battle frontier. I have unfortunately not EV trained him.
This is his stats:

Lvl 88

HP - 302
Attack - 257
Def - 268
Sp.At - 217
Sp.Def - 216
Speed - 123

Moves:
Earthquake
Dark Pulse
Rock Slide
THUNDER


and i need your help. Should i exchange Earthquake with Aerial Ace? So I am covering is 4x weakness? This may be the only way to earn the gold print in Battle Hall, because I will soon have to face the fighting class there. Or do you have any other ideas i can use?

First off, the move you probably want to replace is Thunder, not Earthquake. Earthquake is already an extremely solid move and you need a VERY good reason to replace it. Aerial Ace is not a good enough reason.

Dark Pulse is nice, but if you want to go all physical you can opt for Crunch instead. It's not like you'll be flinching many things.
However, for the Battle Frontier, you definitely want to start from scratch and EV train a completely new Pokemon, then curtail its moveset.

An interesting thing I found out in the Battle Hall is the consecutive records are counted for the species, not the specific Pokemon you enter. Thus, you could enter 2 totally different Tyranitar and continue the streak with either one. (Ironically enough, that is how I got my Gold Battle Hall print; I had a fully physical Tyranitar and a fully special one keeping the streak up.)