I've seen this situation numerous times. What rune/equipment do I need to have in order to get this thing?

I've seen this situation numerous times. What rune/equipment do I need to have in order to get this thing?

There are more ways of doing this one.
Dragon class
The easiest way would be to use a Dragon class as they can fly without any limit. That way you would just have to press A or S to fly, go down and fly to the chest.
I think it's needless to say that this approach will always have 100% success chance as it's impossible to mess it up.
1 Dash 3x Vault Runes and no platform activation
Hug the wall, drop down and dash left immediately, then use triple jump to reach the chest. This is also one of the easiest ways to do this.
Hokage + 3x Vault Runes
This is also an easy way without the need to activate the platform. Simply drop down and use your special ability to propel yourself forward the chest wall, then use triple jump to reach the chest itself.
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There are more ways of doing this, but this three i mentioned are the easiest ones and none of them require platform activation.
Also note that you might actually need only 2 vault runes for second and third solution if your timing is good. But 3x vault runes will help you be 100% successful.
You'll need a Sprint Rune (allows dashing) and a Vault Rune (allows multi-jumping) to retrieve this fairy chest. Basically, hug the wall, jump below the platform, immediately dash to the left, jump again while in mid-air, down-thrust the platform to open it up, and stand on it. Afterwards, double jump to reach the chest.
If you want to do it more safely, have two Sprint Runes equipped. I believe it can be done with one alone but, it's kind of risky.
All you actually need is a single vault rune.
The platform is not a red herring. I beat that room with only one vault and one dash rune equipped. You drop down, use the air jump to put you right above the platform and immediately downstrike it. Land on the top (this does take precision), then double jumpt to the chest.
I didnt even use the dash so this is totally doable with only a single vault rune. (Granted the ways listed above will make it way easier... I just wanted to point out that it can be done very early in the game, without much farmed yet)
hermes' boots, which is sometimes given somewhere within the castle. – Dom Aug 04 '13 at 00:16