My brother and I beat this game, together, as it's damned near impossible by yourself. It is indeed really, really hard. However, it's significantly more difficult in Double Dragon II to throw yourself over a cliff - thus why you're given extra lives, I'd imagine.
Further into the game (3rd level, I think?) there are two (three? it's been a long time) bosses which, if you beat them, will join your ranks. There's a squat (short and fat) Chinese man that has a pair of metal claws which he can use to attack (I can't recall if they're unlimited or not) that are roughly as powerful as Bimmy and Jimmy's dragon kick (anyone catch that joke? :P) .
Then in the next level or two, you're potentially aided by a ninja that can jump quite high, has ninja stars (not unlimited, but they might replentish themselves? I don't recall) which are more powerful still, iirc. He's also got a 'flying knee to the junk' kick, iirc.
I seem to recall being able to get continues in DD3 by beating a level, too, though this could just be my memory failing on me. Some of those levels are really, really hard (I seem to recall the ninja level being the most difficult - imagine the two helicopter ninjas in DD2, and you'vegot a pretty good approximation of what the DD3 ninjas are like).
I seem to recall the violent sound effects being fairly lacking compared to the second DD game, however. There was just an incredibly satisfying "pow" sound when you hit someone with an uppercut or dragon kick, and throwing knives made a nice wet-sounding smack. Not to mention the lovely "I've been kicked in the balls" face that the sprites made. I don't recall the sprites in DD3 being quite as well thought out.
Alas, I don't recall if I ever played DD1.
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Socialism and communism better explained by a psychologist than a political theorist.