Most speedrun categories focus on sheer speed, for obvious reasons, but there are some less-popular offshoots that create unique challenges just to push the boundaries of the games (and the people running them).
I think the A button challenge focuses on reducing the number of A-presses above all else, so it's not a speedrun proper. There is a really fun type of speedrun called low% where the goal is to complete the game with as low a "completion percent" as possible (e.g., minimum items collected, quests and bosses completed, etc.) and do it as quickly as possible. But a run that's technically slower with a lower% will "beat" a run that's faster with a higher%.
That's where you get Twilight Princess speedruns that can take more than 24 hours to complete. Although I believe the current record is actually just under 16:
(For those who don't want to watch an entire video: the secret sauce here is a glitch with Link's "item get!" animation that verrrryyyy slooooowlyyyy pushes him backwards in space every time it loops. So if you open a chest and leave the animation running for hours on end, you can phase backwards through walls and bypass the need for keys/progress checks/etc. Which is perfect for a low% run where the goal is to bypass as many things as possible.)
I think the A button challenge focuses on reducing the number of A-presses above all else, so it's not a speedrun proper. There is a really fun type of speedrun called low% where the goal is to complete the game with as low a "completion percent" as possible (e.g., minimum items collected, quests and bosses completed, etc.) and do it as quickly as possible. But a run that's technically slower with a lower% will "beat" a run that's faster with a higher%.
That's where you get Twilight Princess speedruns that can take more than 24 hours to complete. Although I believe the current record is actually just under 16:
https://youtu.be/v2nRW3wKnVY
(For those who don't want to watch an entire video: the secret sauce here is a glitch with Link's "item get!" animation that verrrryyyy slooooowlyyyy pushes him backwards in space every time it loops. So if you open a chest and leave the animation running for hours on end, you can phase backwards through walls and bypass the need for keys/progress checks/etc. Which is perfect for a low% run where the goal is to bypass as many things as possible.)