For instance, to get the “catch shiny Pokémon” achievements in Pokémon Crystal (https://retroachievements.org/game/11841), you have 1/8192 odds on encounter… for each Pokémon, and there are 213 of them.
Being able to beat a game while not using a core system can be a sign of good game design, or an exceptionally skilled player. Look at Super Mario 64 and speedrunner's ability to finish levels with a single press (but not release!) of the jump button.
That being said, I'm not asking for it to be removed or anything. It's just not something I'm ever going to try to complete myself (maybe I'll manage it on accident). Clearly 4.5% of the people who have played the game with Retro Achievements have managed to pull it off.