Anyone familiar with the Braaaaains achievement from the Zombie Island DLC will have a fair idea of what is in store for this achievement!
The first mission you are given in the Revolution DLC is from Patricia Tannis. She wants you to collect 6 Claptrap Parts which are scattered around the Hyperion Dump nearby. This is simple enough as each of the items is marked up on your radar. You'll come across a few enemies to kill as you make your way around the dump but nothing too taxing.
Take these back to Tannis and you are given a second mission, which is to collect a further 42 Claptrap parts from the dump, except rather than being marked up as collectables, these ones are simply obtained from dead claptraps... that you have killed. Much like the brains in the zombie DLC.
Head back to the dump and head left to the area marked on the map (where the 6th part was from the original mission), and you should find around 50 claptraps waiting for a fight. Most of them will give up a part (be it Wires, Gears or Motherboards) when they die, so if you are lucky you should be able to score all 42 in one visit (if not see below).
When you turn in the mission.... you've guessed it. Tannis wants you to go and get another 75 parts, then another 100, then another 150! After that you're done.
The technique I used to speed (sort of) through these missions was simply to head to the dump, kill everything in sight and collect the parts (usually between 35 and 40), then save the game, exit and reload, guaranteeing a fresh set of claptraps each time. This method allowed me to get the 75 parts in 2 reloads, the 100 in 3 reloads and the 150 in 4 reloads.
By the time I had cashed in the last mission I was down to just 6-7 minutes per reload, so I guess the whole thing may only have taken just over an hour using the above method. Having said that, I did have a very helpful Bloodwing (with Level 5 Explosive Wing) who did most of the killing for me while I just ran round and picked up the parts.