Once you reach the Arcade you must power up 3 arcade machines by using the machine on the left.
For this achievement the handle on the machine needs to be in the UP position against number 1. Then jump on the bike and tap A rapidly to power up the Space Invader machine #1
Simply play this game by defeating the Space Invaders and once you reach a score above 1000 the game will end and you will recieve a Gold Coin
Now before powering up the next machines simply jump back on the bike to power this machine back up and replay it. You will not recieve any more coins from it but you simply need to repeat this process and compete the game around 3-4 times and the achievement will unlock once you have destroyed 500 Aliens. This shouldn't take longer than a few minutes