To me, beating the game is beating the game's final boss, which in this case I label as the boss you face at the rank 5-2 mission. However, I'll believe I've completed the game when I do this:
Rank 30(all 3 flags)
Zilart Completed
Promathia Completed
All jobs to 75
All AF2
It's very hard to say what is "completing" an mmo, but this is what I believe what I need before I quit the game.