Play the card Exchange and have another activate it to beneficial results to yourself.
Firstly, although the achievement image depicts the Reverse Attribute Field card's graphic, it has nothing to do with that. As per the description, you must at some point in a match lay the trap card Exchange, and if someone hits it, you must obtain more stars - and possibly more cards - from the exchange than you initially had that turn. The positions exchanged have no bearing on the achievement.
Rigging this achievement in single-player requires a different sort of playstyle: Begin by selecting a 'weaker' character, for instance Aru, Saki, or an enemy character. Play on a smaller map like Practice Field with Charity and Miracle enabled to ensure you have a better chance of drawing your Exchange. After hitting your first norma and preferably once you have an Exchange available, cease attempts at winning, and simply attack other players until you've lost sufficient stars to put you in last place in the match. Then try to hit an enemy base, either randomly or by attacking a player as they turn in a norma, and place your trap. Keep in mind where you placed it, and actively avoid the spot until the player whose base it was comes home to roost, or another player randomly hits it. Since you're in last place, any player should do. Once they hit it, your stars will be exchanged and the achievement will be awarded.
Sadly, this card isn't very popular in multiplayer circles, and as such, you may quickly find that online players aren't willing to go along with helping you attain this achievement. It is thus advisable to attempt this among friends instead.