The Virtual-On type game in Xenosaga: Episode 1. It’s completely optional, and completely full of options for something so separate from the main game. You don’t have nearly as many mechs to choose from as in the fighting game minigame in Xenogears (which is another one of my favorites), but you can customize their weapons in ways that make this a better reason to collect them all than the battles in the main game are.
“Worst forced minigame”
Specifying “forced” because the more optional something is the more ignorable it is.
Final Fantasy X has some truly terrible ones that are only semi-optional, though, considering you have to play them to get the celestial weapons. The lightning dodging one is just ridiculous.
But my least favorite of all is completely required; the “make Bowser sneeze” minigame in Mario and Luigi: Bowser’s Inside Story. Actually, the giant Bowser battles are pretty bad too, or at least excessively hard compared to the rest of the game.