I think it was a real crime to sell those shitty handhelds... I never played one for more than a minute-- you were lucky if you could tell what the fuck was going on.
I had one of these. Specifically the Tiger Handheld version of Double Dragon.
COMPLETE WALKTHROUGH FOLLOWS:
1) Walk to the right
2) There is a guy.
3) Punch the guy.
4) He dies, and is instantly replaced with another, identical guy
5) Actually, it might be the same guy, who didn't die but just flickered for a moment because of your punch. It is unclear if this game is about fighting an army of guys or just one flickering, immortal guy.
6) Continue punching guy(s) until the battery runs out.