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When your opponent launches your character into the air with a launcher(Called a special attack in this game. It's what the special attack button(S) does while on the ground.) after they hit that character once with another attack while in the air, they can press a direction on the D Pad and the special attack button to do a Team Aerial Combo and send your character flying in a certain direction, do damage to them(Does more depending on which way they sent them) and switch out their current character for the next character on their team to continue the combo.
What you have to do is predict what direction they plan on knocking your character with their Team Aerial Combo and repeatedly press the direction and special attack button, and if you get it right when they go to perform it, your character to emit a burst of energy that will allow you to escape the combo, knock the enemy back and do a little damage to them. That's all there is to it, and after the battle you should get the trophy.
The 3 directions are Up + S, Left / Right + S, Down + S. It's not too hard to do, but smart opponents usually hardly use this and just spike your character down for the OTG if they can get it, or pick a direction that doesn't coincide with the best option for them given the situation.