Plants vs. Zombies

Gargantuar are the biggest zombies and carry a small gremlin type zombie on their back.

The first time you will find them is on the roof levels which is near the end of the adventure, level 5. They can easily be killed with two hits from a cherry bomb or Jalapeno, regular fire from other plants also does damage to them.

Another way to find and kill one is to play co-op bowling which is accessed from the menu co-op menu (needs to be unlocked). During this game mode it is quite easy to kill them if you focus your fire on them and save up the red wal-nuts to spam the Gargantuar with.

This achievement can be made much easier by buying the gutter cleaners (the lawnmowers of the roof levels) from Crazy Dave so that even if you don't have enough fire power to kill the Gargantuar the gutter cleaner will kill him anyway. Thanks to LunarKnightX for the information.

This achievement unlocks on beating your first Gargantuar, simple as but you are able to pop it sooner than you would in story mode if you have someone to play with as he pops up up in the co-op bowling challenge which unlocks before meeting him in the story. Play the challenge as soon as you can and pop the 2 achievements in one go (ZFF's 4 Evr for completing the co-op bowling challenge also)

The Gargantuars are a quite easy opponent to kill if you have the right stratergy. They can be found just over half way through the roof levels(level 5's) so they are quite near the end of the whole adventure.
They can be killed by two cherry bombs but they take time to reload so you can use a smasher or jalapeno. But any plants can damage them. Also if you buy the cob cannons from the shop they can kill them quickly(two hits to be precise).
You can also find them on Co-Op bowling. Easy to kill on that, about 4 hits with the wall-nuts to kill them.
Gargantuars are strong though, they can smash down your plants in 1 hit. And they carry a small zombie which they throw if you take too long to kill the Gargantuar. So its best to kill the Gargantuars fast.

This achievement can be unlocked by either playing through the roof level and killing it there or killing it in co-op wall nut bowling.

Here's a vid: