To get the second new screen, you must defeat all the Cups in Round 2.
Gutsy Golbat: Golbat and Crobat
ClearCut Challenge: Scyther, Pinsir, and Scizor
Barrier Ball: Mr. Mime
Topsy-Turvy: Hitmontop
Furret's Frolic: Furret and Girafarig
Pichu's Power Plant: Pichu, Elekid, and Pikachu
Rampage Rollout: Donphan
Tumbling Togepi: Togepi and Omanyte
Egg Emergency: Chansey
Streaming Stampede: Cleffa and Igglybuff
Delibird's Delivery: Delibird
Eager Eevee: Eevee