In order to unlock this achievement you must win a round while in Pandora Mode 300 times. Pandora Mode is activated by pressing , , + when your vitality gauge is under 25% to activate Pandora. When you activate Pandora, your partner's strength will increase exponentially. The power of the character who calls upon Pandora is necessary to fuel the technique. By sacrificing their vitality to Pandora, their partner will be able to enter Pandora mode. In Pandora mode, the Cross Gauge will be filled to maximum capacity, and you will be able to use EX and Super Arts infinitely. However, if you are unable to defeat your opponent within the time limit it will result in an automatic K.O for you.
You'll want to utilize the handicap option between character select and stage select. Switch the handicap of both players to 25% then start up the match. At the start of the match go into Pandora then use your character's Super Art for easy progress for this as well as progress towards The Trump Card.
To check your progress for this achievement, go to Player Data at the main menu. Select Player Records and scroll down to see how many Pandora Finishes you have to keep track.