The monster Culex is a Superboss from the Squaresoft SNES game, Super Mario RPG: Legend of the Seven Stars. He is a secret, extremely hard boss that Mario and his team don't have to fight. He is encountered by buying Fireworks in Moleville, trading them to a girl in Moleville for a Shiny Stone, and then using the Stone on the mysterious locked door in Monstro Town.
Culex is meant to be a reference to the Final Fantasy series, a popular series of RPGs made by Squaresoft. Contrary to popular belief, he does not appear in any Final Fantasy game. The style of sprite is simply the same as those found in SNES Final Fantasy titles. The reference is also in the music, where the boss theme from Final Fantasy IV plays, as well as the traditional Victory theme.
Little is known about the Culex character. Apparently he consumes time. He is accompanied by four elemental crystals (themselves being a reference to the Final Fantasy series which often features crystals associated with the elements) in battle. Players who manage to defeat him are rewarded with an item called the Quartz Charm.