Yes, you can! And it's actually exceedingly simple to do, requiring very little set-up or skill.
NOTE: By technicality, this skip is a glitch, so before attempting to do so, you may want to turn off autosave in your options and make a manual save just in case. We've successfully done this skip ourselves and had no problems, but that doesn't mean that you won't.
How to perform the skip
To start off, go to the spot shown above. Slide across the ice directly upward to reach the base of Candice's raised platform, as shown below.
From here, push your left thumbstick up. As expected, your character will attempt to go up the icy slope and slide right back down.
Then (while still holding up) slowly push your left thumbstick to the right to begin moving diagonally. When you're close, your character will begin spazzing up the ice slope a bit before settling back down.
If you push too far right, you'll slip off of the slope and immediately slide to the right. If this happens, don't worry—it's a fast reset. Just slide directly down to return to the start so you can try again.
When you succeed, it'll look like you've just walked up the icy slope. Our suspicion is that doing this tricks the game into thinking you're walking up the stairs. Regardless of why it happens, you've just skipped the whole puzzle and have gained the right to challenge Candice!
For help beating Candice once you reach her, go check out How to beat Candice in Pokémon Brilliant Diamond and Shining Pearl on Pro Game Guides!
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