Remember that room you encountered with the four shutters? It's pretty close to the entrance, actually. If you go north, the old man (In Zelda 1 that character's name is Abei) will tell you that strange enemies hold the secret. This is the hint. When progressing in the direction you can travel without the bracelet (which is currently the only direction you can travel) you will encounter a room with rabbits (Pol's Voice), knights (Darknuts), and some other kind of enemy (can't remember which). Note the solitary bush in the corner of this room.
Do NOT fight the enemies. Instead, avoid them and burn the bush with your blue candle. The Power Bracelet is within.