A sub-game of The Legend of Zelda: Ocarina of Time. You can get to this sub-game by getting Epona, clearing Gerudo Fortress and heading up to the range behind the hideout.
The maximum score for this game is 2,000 points for 20 bullseyes, which has been obtained by various people.
As for all Ocarina sub-games, records for Horseback Archery are hosted by N64HS at [1].