Special Victory Condition Description
Hat Trick
Have one player get three kills on the enemy queen without dying.
Kill the queen with a laser to the head.
That's Amore
Have the entire moon in the hex [victory screen]. Not necessarily military, but is currently the only way to accomplish this. Because Split Juniper is the only map with a moon currently, this is the only special victory condition that's restricted to one map (although Headshot is obviously impossible on maps with no gun gate). Liquid Bit's Mike hinted at this condition with the line "when the moon hits your eye like a big pizza pie..." here.
Non-stop Snail
Does not actually mean without stopping, it means without having the rider die or jump off.
Family Portrait
Have every player of the winning team in the hex.
Family Reunion
Have every player in the hex.
On Fire
Economic victory when one player throws in all 12 berries (no dunks).

History of On Fire

This condition was not known to exist for a while, although a few people were suspicious that it might, because we had no special condition for economic victories. Brice confirmed it here, and the first recorded appearance was by LobsterBuster here, eight days later. We still don't know exactly when it was implemented, although the first known mention of a basketball-related win condition was 4 months prior to release here.