Shy Boy is spawned right after the battle begins, followed by some Squire Rels. Once the base is hit, another two Shy Boys, some Mooths, Teacher Bears, Hippoes will appear. Once the enemy base's HP reaches 128000, Assassin Bear will spawn.
As Shy Boy spawns immediately, you should immediately slow his progress with Macho/Mohawk Cats and Wall/Eraser Cats and work on it from there. Try to keep some units ready if possible and save your Cat Cannon for the Assassin Bear. The moment you see Assassin Bear, don't hesitate the use the Cat Cannon, otherwise it'll wipe out all of your cats very quickly before you even realize it.