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Neo 4
As with the previous level, not all the details for the curling stone route is shown here, but only what I consider to be the most crucial areas. In this level, you need to hold curling stone fairly deep into the level, and the lava will instantly break your powerup. As a result, avoid taking damage twice in quick succession.
In the second room, there are some curling stone jumps that just manage to clear some gaps. There is a really wide gap, and it seems that the best way of dealing with this is to jump with curling stone, and then float towards the platform.
In the Dedede section, there are thick columns that require either two uncharged hits or one charged hit. The charged hit is faster, but for the column guarded by a Gordo, it's significantly easier to swing twice. Shard 1 is hidden at the top of the column, and you can reveal it by jumping over a pit of lava with a charged hammer.

Towards the end of the room, there are three enemies that block the exit. Either swing at each of them (middle), hoping that the last two enemies are close enough to take out with one hammer, or damage boost off the Bronto Burt (right), allowing you to just walk through the middle enemy.
The next room is mostly flat, but there are two key areas. There are three enemies in a row stuck in a pit with a block on top. It's best to use the curling stone and bonk on the bottom of each block to avoid both falling into the pits and bonking off the sides of the blocks. In the section with lots of lava, I don't have anything better than puffing after each curling stone.
Finally, we reach the barrier blocking Shard 2. Underneath the barrier is a pool of lava, so if you have enough health, you can jump right into the barrier with curling stone and grab the shard. If you're at 1HP, you can still break the block without taking damage. In my opinion, the safest way of doing so uses the "ice shavings" generated by the tail end of the curling stone.
In the next room, combine for double fire off of any of the three fire enemies towards the beginning. The rest of the room follows a standard route. At the end, you can optionally get single fire, making the Magman fight safer.
Float up and grab Shard 3. Once you reach the three rows of blocks, the strategies diverge a little. If you have double fire, throw it away into the blocks and float up. Grab cutter from the Fishbone and exit out. If you have single fire, headbutt the rows of blocks and combine carefully for fire sword. One safe thing to do is to put your fire powerup in your mouth. That way, if you accidentally climb a platform underneath, it won't break.

Overall, double fire is faster: no need to pick up single fire, breaking the blocks is quicker with the double powerup throw, grabbing the Fishbone is quicker, and there is little to no timeloss for getting fire sword during the Magman fight.
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