Unfortunately this one involves quite a bit of luck. The Wild Card tag appears in all modes and all rounds where you can spin the wheel, but it only appears once. If another player/CPU picks it up, even if they go bankrupt, the tag is gone. If you're exclusively going for this achievement, it'd be a good idea to restart your game and cross your fingers that you land on it.
Once you successfully collect the tag (land on the wedge and successfully pick a consonant) 5 times the trophy will pop. You do not need to solve the puzzle with the tag to count... even going bankrupt and losing the tag will still count as 1 of the 5 that you need to collect.