Location:
End of Dungeon 1: The Eagle.

Attack Pattern:
Aquamentus moves slowly from side to side across the top of the screen. It periodically stops to spit three fireballs in a spread pattern towards Link.
Weakness:
Its head. Any direct hit to the head with the Wooden Sword will damage it.
Strategy:
Stay mobile and position Link diagonally from Aquamentus to avoid its fireballs. When it stops to attack, quickly move in and strike its head with your Wooden Sword. After landing a hit or two, retreat to avoid its next volley of fire. Repeat this pattern until Aquamentus is defeated. It has relatively low health, so consistent attacks will bring it down quickly. The Blue Candle is not particularly effective here.
Reward:
Heart Container, Triforce of Wisdom Piece 1.