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To get this trophy, you need to kill two Gargantuars with Corn Cob missiles during a single level. This shouldn't take much longer than half and hour.

Other guides suggest doing this on the Roof level 5.8. However, since the game has no level selection for Adventure Mode, I'd suggest doing this in Survival Mode(Survival Endless) instead - at least if you've already completed the game.

Clarifying information:
You need to plant two Kernel-pults next to each other in the same lane to be able to upgrade them to the Corn Cob.

It doesn't matter if it's a normal Gargantuar or Giga-Gargantuar(stronger, red eyed versions), nor does it matter if they are weakened by other means first: You just need to deal the killing blow using the Corn Cob missile. You also don't need to hit both with a single missile. As long as you kill two with Corn Cob missiles in a single level, you should get the achievement.

Since Survival Endless has randomized hordes of enemies, the below plant setup is just a general idea of how to set things up. It's also far from the only way to do it, but it's what I did. You'll have to take into account some changes and some additional defenses based on what zombies will appear in the next wave.

General how to:
1. Start Survival Endless, and make sure you've bought the Rake from Crazy Dave.
2. Then plant Sunflowers, preferably in the second column to avoid Diggers and Catapult Zombies.
3. Followed by some Lily Pads with Cat Tails on them. Next get some Melon-pults next to the pool, and upgrade a couple of them to Winter Melons.
4. Plant two Kernel-pults on the top lane and the bottom lane, then upgrade them both to Corn Cobs as soon as you can, while still making sure to set up defenses against any zombie types in the waves.
5. When a Gargantuar appears, fire both Corn Cob missiles directly at it by clicking the Corn Cob and then clicking on the ground in front of the Gargantuar. Two will kill a normal Gargantuar, but not a Giga-Gargantuar, so if you encounter those first, let them take some damage before you fire the Corn Cobs.
6. If you killed two Gargantuars in one level(ie. between getting to pick what plants to use), you should now have the achievement! Congratulations!

And again, since the enemies are randomized, you might get lucky - or unlucky. But generally, the above way to do it should get you the trophy as soon as any Gargantuars start showing up.