Here is how you unlock the achievement “8 Bit Hero.”
The exact score
To unlock the achievement, you need to reach the score of 5020 in the Fear Trap Arcade game located in the Drug Store.
It took me around 3 full level clears to reach this score, while only hitting the fast optional space enemy at the top only 2 times. If you need to you can go further, as I could still continue to play as long as I didn’t lose any lives.
Hopefully this guide was helpful, and good luck!