The badges don't work because of the Hot Coffee thing. When you open the second browser window, chat (and badges) shut down in the main window, which is where the game keeps track of all this stuff. You have to do all the badge tasks before opening the second window for them to work.
The original version did have a 5 minutes achievement (no. 32, IIRC). It was changed in the version put up on Kongregate, though (otherwise, it would be impossible to get the Hard badge, because 5 minutes is 300 seconds, and you only get 240 to earn the badge).
Actually, the regular Contra code does work (and it canocally ends at the A; only it's use in the original Contra required anything else...the code appears is pretty much every action Konami game, although it's effect isn't always predictable: in Gradius 3 it caused you to self destruct).
 "Achievement Unlocked 2"){kind=icon}
 "Achievement Unlocked"){kind=icon}