On the level "Set the Controls for the Heart of the Negativatron", inputting the Konami Code on the broken arcade machine (Up, Up, Down, Down, Left, Right, Left Right, X, O) will cause it to explode and reveal the numbers '3733 5683', which on a phone key pad spells out "Free Love"
Eve is likely based on the story of Adam and Eve, the original humans who ate the forbidden fruit, often considered to be an apple, which cursed humanity with knowledge of sin. Her name, the bite mark where her right eye was, and that her head is an apple possibly reference it. It could also be a reference to the expression "an apple a day keeps the doctor away", since she's a nurse and has an apple for a head.
In the first level of The Cosmos, Into the Heart of Negativatron, an arcade can be located in the latter part of the first half of the level. The last machine in this area is malfunctioning, and upon entering the Konami Code, will cause the machine to explode.