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Many things in this walkthrough are explained in notes on the video and also in the description below. Please read these before asking questions.
My complete Level 4: Thieves' Town walkthrough for The Legend of Zelda: A Link to the Past. Played in real time on Snes9x v1.43 rerecording with rerecords used to optimize video length.
Equipment checklist: 14 Hearts, Red Shield
You can upgrade your shield (as well as the boomerang) at the Waterfall of Wishing, which is just outside Zora's Waterfall in the far northeast corner of the Light World.
[00:37] Bunny Link
If one of these spinning, flashy things touches you you'll transform into bunny Link for a short time and be unable to use your sword or items. Ironically, bunny Link also cannot dash.
[01:47] Conveyor belt corridor
Take it slow and careful in here and kill the cloud enemies as you go. If you try to run through and dodge everything you'll most likely get trapped between multiple enemies.
[03:10] More conveyor belts
You can walk along the edges of this room without getting carried away by the conveyors.
[04:30] Boss: Blind
Blind has three heads and each time you knock one off it'll start flying around the room while shooting fireballs at you. If you can manage to keep full hearts, stand back and return fire with sword beams while dodging the fireballs. Otherwise, move in close when you find an opening and hit Blind's head with your sword, either from the side or, when Blind moves to the bottom of the room, from above. Never try to swing up through Blind's body because you're likely to get hit in doing so.
I also have another no damage video, that doesn't use sword beams, here:
• Zelda A Link to the Past - Blind - No damage