How skilled is Thorgrim and what kind of boost does the Book give?
I assume Thorgrim starts on the throne with four Thronebearers, and Erza might try to start with a direct attack to him, and slash down the Thronebearers after, which I think shouldn't be that difficult, as they seem to be fodders.
APs counts relatively, Thorgrim will get just small damage, and assuming he is baseline (6.3 megatons) he is about 5 times weaker than Erza's dura (which is around 30 megatons), with the gap increasing with strongest armors, especially the Adamantine.
Erza can outrange him and if she can also outskill him (combinining stamina, senses/reactions, variety and versatility of weapons and general skill) I can see her defeating Thorgrim, maybe disarming him and keep going all out until he finally goes down, or just tire him out without him being able to reply, despite taking very little damage.