How can you reach the treasures of Frozen Castle?

The Frozen Castle in act 2 features a good old videogame trope: ice physics of the "once you step on ice the only way you can go is forward". This is combined with treasure chests, some of which are obviously impossible to reach under these rules, such as the one on the very first floor, which kinda sorta looks like this:

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How can you obtain all treasures of Frozen Castle, both as in the quest and the global dungeon?

Solution 1:

To obtain the treasure on the ground floor of the Frozen Castle quest (the one "pictured" in the question), climb to the third, then from the stairs go up and right. You'll fall down into a side room of the 2nd floor with four more holes. Fall down the bottom left hole and move straight up to obtain your reward.

To obtain the treasure on the third floor of the Frozen Castle quest, reach the heal point by the stairs, then go left one space, up all the way, then left and then up again. This dodges all the pits in the way.

Now for the global dungeon. From the entrance you can't do much but slide all the way to the north wall of the third floor. From here you can fall down four holes. From left to right:

1. (must have defeated all four Ultimate Kings)
   From here, go north to fall to ground level, then south to collect your reward.
2. From here it seems you can only fall through to ground floor. On the south end of this floor, however, awaits a "mini-boss fight", Cozain. This seems to be necessary for later.
   At global level 15, I had to use herb to defeat him (and was left with just a handful of hitpoints afterwards), so beware.
3. (must have defeated the only female Ultimate King. She is featured in the very next quest.)
   From here, go south, right then north. Once on the ground floor, head north for your reward.
4. From here, go north all the way, left, north, right to fall down on the first floor. From there go south to collect your reward.