Most Annoying Sound: The sound when you get hurt can be more than a little maddening, especially when it's followed immediately by the Game Over music.
Polished Port: The Game Boy port rectifies a few things to make it a lot less fake difficult. It adds title screen music, an ending cutscene, an inventory screen to check on Milon's stats (accessed by pressing Select) a password system, a bit more Mercy Invincibility when hit and a few bosses have been given new graphics.
Surprisingly Improved Sequel: Do Re Mi Fantasy, but it accomplishes this by axing all of the first game's Metroidvania elements and turning the whole thing into a bog-standard (but beautiful) side-scrolling platformer.
That One Boss: Every boss in the NES version. They take a lot of hits and throw their projectiles randomly. With no Mercy Invincibility, it's easy to have all of Milon's health drained from one battle.
The last boss was particularly this back in the day if you were a poor shmuck who had a black&white TV. Given the boss has several identical-looking interconnected "floors", or well, versions of the same floor (complete with fake bosses that look and act exactly like the real thing) that were only different by the color palette, it was nearly impossible without memorization and trial&error to defeat the real final boss (unless you just got plain lucky and/or were skilled enough at the game to defeat each one in turn until you stumbled upon the real one).