If you're looking to get the badge quickly, you don't need to kill all the enemies before moving onto the next screen, look at the map and rush to the bosses. All three are easily beaten without any upgrades.
Lots of fun, however it's quite easy, I'd like to actually feel pressured to go protect my base. Apparently there's a "Space station is taking heavy damage" message, (suggested from the comments) which I never saw ever and having played this game multiple times from the past and coming back to it, I still have never seen that message
 "Knight-errant"){kind=icon}
 "Rogue Isles"){kind=icon}
 "Ether War"){kind=icon}
 "Pingy the Ping Idle RPG"){kind=icon}
 "That Pokeyman Thing Your Grandkids Are Into"){kind=icon}
 "String Theory"){kind=icon}
 "Tangerine Tycoon"){kind=icon}
Thanks!