GameFAQs forum says that it's a 1% chance of showing up

I've already gotten the other Safari mons, but got Phione to show up when I put Ampharos in the front of my party.

If you win with 0 moves left, it's a 40% catch rate, which goes up to 80% with a Great Ball (Super Catch activated for me and bumped it up to MAX).

The level starts with an awkward ice arrangement and it freezes stuff over time, so it's a little tricky, I barely won.