Parrots (as named in the credits of Prehistorik Man for the SNES) are enemies from the DOS game Prehistorik 2 and its SNES and GB remake Prehistorik Man.
One also appears in I Wanna Be the Boshy as a hazard in World 1.
How hazardous is it? Edit
Very. Late in World 1, a voice says "Run Boshy! Run like the wind!", and a parrot shows up from the side of the screen. This triggers just a few steps before the Ear Rape Spider. The parrot moves just as fast as the player, and kills him/her on contact. It continues to chase the player for the rest of the level. In the area right before Hello Kitty, it suddenly grows and explodes with splattering blood like if the player died.