The Crystal Skates are unlocked on the second island, after helping Carlos.
Crystal Skates are earned through the main story quest, on the second island of Omninesia shortly after clearing the first gymnasium. You will find yourself owning an elevator key and will head to the Grand Banyan of Citerior Omninesia. You cannot access Ulterior Omninesia proper until you have a pass, so proceed through the Citerior until you reach a cave entrance guarded by henchmen of the Belsoto clan.
The majority of Temtem tamers in Citerior use are nature and fire, so having Temtem with toxic and water damage will be a boon here (however, be careful with your Water Temtem: Nature Tems absolutely eat their lunch. , and there's a handful of Electric Tems in the mix as well). Having a Ganki on hand for the occasional Water Tem isn't a bad idea, and if you've got a Crystle you'll find the Sparzy (s) a few Tamers throw your way around will be of little concern.
Note: Most of the battles leading up to the Crystal Skates will take place in the mid-twenties, so you may need to grind a bit in the tall grass. The nearest Temporium is back in Mokupuni, so you'll want either smoke bombs or the patience of a saint as you make your way through the Citerior.
Once you've reached the end of the trail and the entrance to the Grand Banyan guarded cave, you'll find Carlos hiding behind a rock on the left. He'll ask you to find a way to get inside and give you a pass giving you access to Ulm Onminesia. Return to the elevator on foot or use a smoke bomb to return to Mokupuni. There is a mini-Temporium in the Ulterior, so once you head down and reach it, that will make the coming glove easier to bear.
Push through the Ulterior until you reach a pond with several Belsoto goons enjoying the sun. Take turns defeating each one and you can finally steal the uniforms they have hung up to dry. Return to Carlos at the entrance to Grand Banyan and make sure your Temtem is healed. He'll ask you to put on the uniform, and once inside, you make your way into the Grand Banyan. Treat it like a dojo: it's supposed to be a melting pot, so have balms, resurrected, etc.
Once you beat the blonde lieutenant at the back, you'll flee the Grand Banyan with Carlos, returning to the boulder he was hiding behind outside. For your efforts, Carlos will give you a pair of crystal skates he found inside. Here it is: your own pair of skates to better navigate the red crystal tiles.
There's a huge caveat to this: you don't keep the skates on when you clear the Omninesia. At first it was a huge pain in the ass, as players who completed the second dojo here and moved on to the third island found that they couldn't catch the four leaf clover on the first island, nor that they could access patches of tall grass tucked away in places accessible only with skates.
Crema has heard the angry calls from the Tamers and released a patch to address these concerns: You still lose the Crystal Skates, but you can at least access the Four Leaf Clover without them now. Additionally, Temtem found in those hard-to-reach tall grass patches has been moved to more accessible locations that don't require ice skates.
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