Lock 'n load! It's Contra for NES, developed and published by Konami.
Contra was originally released to arcades but later it got multiple home releases to NES, MSX2, DOS, Commodore 64, Amstrad CPC and ZX Spectrum.
The plot of Contra is that 2 soldiers are sent to an island to stop the enemy forces. You start out fighting normal soldiers, but later enemies do change to nasty ones.
Game can be played solo or co-op, and there is handy weapon power-ups to collect to even the odds against huge amount of enemies.
There is also that famous code that grants you 30 lives to play with, but I'm not using that in this playthrough.