God, I really can't remember with any clarity the first one I ever beat, but my first console was an NES so it would be one of the titles there.
I never beat Ninja Gaiden because of that fucking eagle on that one stage. If you search YouTube you will get an exact video of that one eagle. It is such an insane jump to dodge that fucker and continue dodging it.
So yeah, not Ninja Gaiden.
Not Mario either because I just got to a certain place that I couldn't get past. There was just this forever hole in the floor and I had no clue how to bypass it.
It could have been Robocop because I loved that movie as a kid (JFC who let a kid watch ROBOCOP?!). It was hard as shit though, especially the last level and the ED-209 boss fight.
It also could have been Castlevania II: Simon's Quest. I absolutely adored that game as a kid and I played it non-stop (between Ninja Gaiden and Robocop). I couldn't get enough of this game!! It had the "perfect" difficulty of gameplay, it was just (and to this day remains) really hard to figure out what to do next without enough clues. And half the clues in the game were FAKEOUTS!! SUCH BULLSHIT!!
But I did beat the fucker. When you summon Dracula at the end you can pop a laurel and drop nothing but sacred flame sub-weapon on his resurrection pyre and kill him in like, 5 seconds. rofl
I also had Star Wars and Tiny Toons Adventures. I did beat Star Wars eventually (yoooo those flight sim levels ON A FUCKING NES were doooope). Tiny Toons was also surprisingly difficult later on (Monty's stage was insane, wtf).
OH YEAH DOUBLE DRAGON II. Literally the greatest beat-'em up of all time. Great music, amazing co-op, super hard/fun fights...
In light of the new Castlevania anime, I wish I had Castlevania III. I did have the other Ninja Gaiden games too but really no memory of them like the first game. Double Dragon III was ass... Battletoads to child-me might have been like giving a TikTok'd person a differential equation and telling them to cure AIDS with it.
I can't remember anything else...