Instructions
Go to the tent on the west side of the entrance to Gerudo Valley. You will approach the leader of the carpenters you met earlier in the game. He explains that his workers have been captured by the Gerudo and offers his help in fixing the bridge if his men are rescued.
Proceed westward into Gerudo Fortress and walk within view of one of the guards near the entrance. They will put you in a prison cell -- with all your weapons and items intact, for some reason.
Aim the Longshot at the wooden ledge overhanging the window and latch onto it. Use your vantage point to eliminate the Gerudo with arrows.
Make your way through the Fortress. Use arrows to stun the guards indefinitely or, if you run out of arrows, use the Longshot to stun them briefly and finish them with a sword stroke.
Talk to the carpenters in the prison cells as you encounter them. After the dialogue, a Gerudo will drop from the ceiling. Fight and defeat her for the key to the cell. Use Z-targeting, move around and hold your shield up until you see an opening. If you see the guard crouch and hold her swords across her chest, move -- the unblockable jumping strike she does will end the fight instantly and send you back to the cell.
Rescue each of the four carpenters. Leave the Valley and talk to the head carpenter. They will begin fixing the bridge.