Well, I found a new glitch in this game. (Atleast I think it is.) If you go to a Gate that takes you to Castle A or B and equip the Floating Boots, It'll warp you to each Gate you've uncovered on your map. Simply descend to the bottom of the floor in the room when the boots are equipped.
Watch the movie
Here. I've been playing around and totally found ways to totally break the game. For example, go to the Clock Tower and talk to Death so you can use the Gates. Now go back to the Castle Entrance and go to the Gate that you normally need the Super Jump to reach. If you have the Ice Fist and the double jump you can make it up the platform with ease if you time it right.
From there after you use the Gate you can grab the Lure key which is right below the Gate room. If that wasn't enough, go fight the Pike Master in the Gallery and get him to drop the Floating Boots. If you have the Crushing stone go back to the Entrance hall and go to the shaft that has the metal gate blocking your way.
Destroy it, equip the Floating Boots so you can fly up that one place where you need the Super Jump. From the you can head all the way down and grab the Floodgate Key. For like all of this you need Maxim's Bracelet which is why this breaks the game so bad.
I'll still need it for my run though to complete the game properly. Gah, this game is so confusing. I have no idea of what to do in what order.
Edit: The Crushing Boots and Super Jump seem to be needed to get one of the relics. The one outside the castle to be exact. So It looks like I can't just use the Floating Boots instead...