Crawl

First, you need a sling as a weapon for this achievement. You can hope one randomly spawns in a store for you to purchase, but there is an easier way.

When choosing a deity, if you taunt Gor instead, you will start the game with a basic sling and be unable to buy any other weapon.

From there, just play as normal, until the AI evolves to a GIANT or posseses a GIANT statue (statues can spawn randomly at any time).

Then just kill the giant with your sling.

Update: Thanks to SherlockGecko for confirming: It must be done against an AI. You cannot kill a human-controlled giant for the achievement.