Here is the full list of all 23 Race With Ryan achievements.
Win the Formula Fruit Cup (Easy)
Win 10 races in any mode
Win the Pizza Cup (Medium)
Win the Pizza Cup (Hard)
Win 2 Races
Win your first race!
Win the Hot Dog Cup (Medium)
Win the Hook Prize Cup (Medium)
Race for 1 hour in total in any mode
Race for 2 hours in total in any mode
Win the Hook Prize Cup (Easy)
Win the Royal Race Cup (Easy)
Race for 3 hours in total in any mode
Win the Formula Fruit Cup (Medium)
Win a race in Split Screen
Win the Toys Master Cup (Easy)
Drift for 10 minutes in total
Win the Pizza Cup (Easy)
Drift for 30 minutes in total
Win the Formula Fruit Cup (Hard)
Win the Royal Race Cup (Medium)
Win the Hook Prize Cup (Hard)
Win the Royal Race Cup (Hard)