It makes sense to unlock this as one of your last achievements since you'll obviously get a lot of kills by playing the game normally. It is cumulative and your stats seem to update whenever a loading screen occurs.

Farming instructions:

• Play Oasis (TFE) on Normal difficulty or higher.
  
• Play up to the infamous "frog room" near the end of the level and save your game to be safe.
  
• Now enter the room, trigger the frog fight, and perform a rocket jump to get up to the "balcony" that surrounds the arena (jump and fire a rocket at the ground below you).
  
• Stand back and let the frogs spawn. I recommend equipping the Tommy Gun since some frogs may randomly bounce up to your location. Wait until they stop spawning or until enough have gathered below you. Bait them back if they start jumping away.
  
• Equip the Rocket Launcher, stand close to the edge of the balcony, and save again.
  
• Kill the frogs with a rocket (or a few) and load your saved game. Repeat this step.

Using this method, I can get about 140 kills with one shot. You can use similar strategies in other fights against frogs or kamikazes (e.g. at the end of Metropolis) or with Serious Bombs (e.g. at the beginning of the Grand Cathedral) but this one works very well. One of the comments below suggests using the Serious Bomb at the end of Crystal Cove (Bright Island) for 250-300 kills. Someone has also mentioned that your progress is disabled on Workshop maps.