Here's some creenshots of the 2nd minigame:
How it works:
Different Pokemon have different speeds, and require differing amounts of charge to defeat. For example, Gyarados is extremely fast but doesn't require much charge due to his double-weakness / Dragonite is medium speed, but due to his Dragon-type negating his Flying weakness, he requires a lot of charge to defeat.
Also, each Pokemon has a random chance of being catchable. To catch them for bonus points, you have to repeatedly click them - which can be difficult if you need to be charging a bar at that particular time.