Dig next to a flower to get an extra life.
Destroy the Benemoth building. You should hear a foghorn sound to indicate that the hat has been unlocked.
After fighting the Boss (giant green robot with the eye and a fork and knife) and his life reaches zero, he will start exploding. Continue shooting at his eye. He will just continue exploding as long as you shoot, and you will continue gaining points. You can stop when you have about 60,000 points. At the end of the level, you will gain about seventeen lives.
Area 51 Hat: Get to level 3-1.
Blond Hair: Beat the final boss using hard difficulty.
Diamond Tierra: Beat Level 2-2 using hard difficulty.
Jouster Hat: Beat Level 3-4 using hard difficulty.
Private Eye Hat: Beat Level 3-2 using hard difficulty.
Soviet Union Hat: Get to level 2-1.
Successfully complete level 1-5 and the Super Soviet Missile Master mini-game will be unlocked after the intermission sequence.
Having completed the Level 1 Stage 5 area you will unlock the Super Soviet Missile Master mini-game.
In the Options Menu, where you can rename your alien, use the following names to unlock hidden hats for the 2 player game: