As you play through the game you will pick up key items associated with the 6 different summon magics in the game with the first one being
Once you have gotten your first key item you have the ability to get this achievement. During battle encounters if you are getting beaten badly enough you will see the option to press LT to summon. You must be low hp and possibly have one or more of your party members dead.
You must hold LT for a few seconds and you will summon one of the six to aide you.
I have not noticed this happening in boss battles.