It is mostly based on luck, but if you find a Plantern, use it in the center of eight vases, so there will be a higher chance of finding the Gargantuar. If you want to, you can restart if you do not find it. Doing this each time will increase the probability of getting Plantern.
Trivia
The Imp on the Gargantuar vase in the achievement's icon appears to be naked.
The Gargantuar vase on this achievement's icon is similar to the unused vase with a zombie face, or the purple vase that always contains a Vase Gargantuar from Plants vs. Zombies 2.