The Garbage Collector can be fought by skipping 2 Cargo ships (the ships that drop weapons each round) in a row. 2 in the same wave, or 2 across 2 waves are both acceptable. When you let a cargo ship go by, you will see an animation in the background of the ship flying away. After the 2nd in a row, you will see an animation of the Garbage Collector flying across the background of the screen (a small green ship) to notify you that you will face him at the start of the next wave.