Despite the different name, Grothia is really just Ifrit, so you will know what to expect. Similar to the Belgemine battles, you cannot use your own Ifrit here, so you will have to choose another Aeon. Also, Grothia will absorb Fire, but he isn’t weak to any of the other elements, so there is no sense in summoning Shiva, unless you want to worry about healing her more often, because of her weakness to fire. At the beginning of the battle, Grothia will have a full Overdrive gauge, so he will use Hellfire. Outside of that, the other attacks he will use are his normal one and Fira; Grothia doesn’t seem to use Meteor Strike at all.
Bahamut is a good choice to use against Grothia, and you should use Shield before his first turn to mitigate the damage from Hellfire. It’s better to not use Impulse with Bahamut, as it causes a bigger delay than the other moves in his arsenal, so stick to the strongest spells, like Thundaga, Blizzaga, or Waterga. Remember to avoid using Firaga, since Grothia will absorb it and you don’t want to make the fight any longer than needed.