The first boss in the original The Legend of Zelda (1986) is Aquamentus.
Aquamentus guards Level 1, “The Eagle,” the game’s first dungeon. It is a dragon-like monster with a prominent horn and three heads that periodically fire three projectiles across the room. Defeating it rewards Link with a Heart Container and the first fragment of the Triforce of Wisdom.
Aquamentus is often confused with Gleeok, another dragon-like boss from the same game. Gleeok appears in later dungeons and has multiple detachable heads, while Aquamentus is the boss of the opening dungeon. The original game also reuses Aquamentus as the boss of Level 7, “The Demon,” making it both the first boss encountered and a later repeat encounter.
The name also appears in Oracle of Seasons, where Aquamentus returns as the boss of the first dungeon, Gnarled Root Dungeon. That later appearance can make the character seem less exclusive to the 1986 game, but the answer to this question remains the same: Aquamentus.