The first 4 stages are:
To unlock Ash's PokeCar, you have to kill 70 enemies in one game on Story Mode.
To unlock Ash's Shocker, you have to defeat Boss 10: Brock in 10 shots.
To unlock the London Tipton character, avoid 30 texts in the "Phone" stage.
To unlock "Phone", defeat Team Rocket in Story Mode level 7.
To unlock Stage V: Wartortle's Paradise, pass Wartortle in 7 races.
More spoilers at COMPUTING.........