Duke Nukem Forever

This can be obtained in the strip club level.

Upon entering the club make you way through the main "show room" and enter the games room through the curtain, make your way through
this room past the air hockey table and to the right you will find the Alien Abduction game.
The game itself is identical to the whack a mole games that are usually found at funfairs and merely requires you to hit each Alien once it pops it's head up, you must pass all five waves to complete the game and upon completion you will get the achievement.
I found the easiest method was to leave the cursor in the middle which covers 3 of the mole positions with only the slightest of movement with the right stick, you then only have to worry about reaching the ones at the far right and left of the game, however they are fairly slow moving until the last wave and so you should have no problems in hitting them.
You can afford to miss up to 2 aliens and still pass a wave, any more than that and you are unlikely to get a sufficient score to continue to the next wave.
I hope this helps, any questions please drop a comment and I will try and answer as best I can.

Go to the strip club level, to the game room.

In the back right corner is the Alien Abduction game... essentially a Whack-a-Mole type game. The goal is to hit each alien that pops up. The tricky part is that you use X to hit, not your trigger.

What worked best for me was to use my right thumbstick to aim like normal, but instead of using my right thumb to hit X, I used my left thumb. That way I could move around quicker. There's also no penalty for whacking at the wrong time, so spam X with your left thumb.