Furrygon

When it appears

As a tier-3 Nexomon, it only turns up in the grass after you beat Ross and Nora in Laboratory Ruins Boss, or from the start in Custom Mode with high-tier encounters allowed. During the main quest Resurrect Bolzen, from when you talk to Derek in Underwater City Ghetto or reach Logan's Shack until you complete it, Furrygon is one of a set of dragons that replace the wild Nexomon on some maps.

Capturing

Its favourite foods are Green cake, Baguette and Taco, Flotter's, as every stage of a line shares the first one's. Feeding it one adds 7 to your capture chance, where other food adds 2. As a dragon, it's harder to capture: food counts for less, Nexotraps count for half, and wearing it down adds at most 15 instead of 20. A Golden Nexotrap still adds the full 100. Catching a Nexomon explains how the whole chance adds up.