Once you reach the Sanctuary you will be able to interact with Clap Trap for quests. He will reel off requests that would be almost impossible and extremely boring to complete But once you accept his quest, return to him and hand in the quest. He will insist on sharing the stash with you anyhow.
After you hand in the quest, he will scurry off. Just follow him until he starts bumping into a dweller nearby. You will now be able to walk up to him and request a high five by pressing "y". After this he will start to bounce up and down in place, then all you have to do is melee his hand.
Clap Trap can be found on the left hand side on the way in behind Scooters garage and just across from the medal center. You may need to melee Clap Traps hand a few times as it doesn't always seem to register.
If you happen to be playing with a friend, and they perform the high five, only they will be rewarded with the achievement. So either be first to high give Clap Trap, or go back to playing in single player an do it on your own.
If you're having issues with method, just progress through the main story. You will need to obtain an upgrade for Clap Trap. Once you do, return to Clap Trap in Sanctuary. Once you issue the upgrade, he will ask for a high five.