Mystery Goomba

The Mystery Goomba is a Goomba that has been spawned in the Bowser in the Sky level of Super Mario 64 that's viewing can only be done via extreme precision. This Goomba cannot be harmed via normal means.

Deconstruction
In the coding of Super Mario 64, there's an object spawner that summons three Goombas in its radius. This spawner unloads the Goombas once Mario is away from this radius. The spawner that contains the Mystery Goomba in Bowser in the Sky is this type of spawner, as two Goombas are in the radius of where the Mystery Goomba should be.

The precision of viewing the Mystery Goomba is the way it is because in an "unpersonalised" copy of Super Mario 64, it is not on any platform it can stay on. All Goombas have their own activation radii too, and Mario must be in the radii in order for the Goombas to activate. The requirements for the triple object spawner Goombas to be activated are to be on both the activation radii of the spawner and the Goombas themselves. Since the Mystery Goomba falls down due to having no platform to stand on, the radii of it is mostly away from the radius of the spawner, and Mario has to look with precision in order to find the Mystery Goomba right before it despawns.

Defeating the Mystery Goomba on an "unpersonalised" copy of Super Mario 64 is most likely impossible due to these factors alone. Without the use of modifications or the personalized AI, this is certainly the case.

Personalisation
Since the Mystery Goomba is an entity that's in the vanilla copy of Super Mario 64, it is also affected by the personalisation AI of the game. Through Dynamic Level Rearrangement, it is possible for the Mystery Goomba to be tangible for Mario to defeat. It can also be affected by Enemy Discoloring as well. It is much more common to see the Mystery Goomba as a side effect in a personalized copy of Super Mario 64 due to all of the contents being there for it to spawn.

With the use of Dynamic Level Rearrangement, it is also possible for Goombas that are spawned in other locations to become like the "Mystery Goomba". The requirements for it are that it must be on a level that contains a death barrier and bottomless pits.

Trivia

 * The term "Mystery Goomba" was coined up by the YouTuber Pannenkoek2012.