I was able to clear a loop to rescue Donkey Kong from the evil Mario on both game modes, so I'm calling this beaten.
I guess the old arcade convention of having a handful of stages (4 in this game's case) and then repeating them until you either run out of lives or get bored isn't a big draw for me anymore. I also wasn't a fan of the stages, especially the 2nd stage. Since the loop number is only one character long, out of curiosity, I used save states to get by Loop 9 -- it goes on to Loop A (presumably going to Loop Z).
I ran into a couple technical issues, which might be a result of the Classic Edition's emulation. On the 4th stage, sometimes when I'd hit the apple on the right, the apple would glitch and either part or all of it would still appear on screen. I had a few times where enemies would simply disappear. On the first two stages, jumping over enemies would rarely grant the 100 points. The game also crashed once, giving a C7 error code, which apparently is a code for the game not being compatible with the emulator (I haven't hacked mine).