To get this, follow the instructions of the achievement and kill a Gargantuar in Garden Ops Mode. They don't always spawn but they are part of the boss rounds.
Note: Only the normal Gargantuar and counts towards the achievement (!). The strong one (wearing sunglasses) is a Giga-Gargantuar and doesn't unlock the chievo. (Thanks to
xPut Name Herex for the tip)
You have to be the one giving it the final blow. So if you're really trying to grind for this achievement let your teammates lower his health and just as it starts to go very low attack it (or use a super attack like the sun beam of the sunflower - that's how I got it).
I think they are pretty easy and not very strong since they move so slowly.
Edit:
It appears that this achievement is for some reason glitchy. Since the instructions of the achievement are not 100 % clear, maybe you don't actually have to finish off the Gargantuar, but you have to deal the most damage to him. Try this, if you still haven't unlocked the achievement!
Also a tip from
iLag1337: Try not using potted plants against the gargantuar but defeat him entirely on your own.