Here is the full list of all 12 Dog Sled Saga achievements.
Have your rival offer to be an employee
Qualify for and join League 7
Qualify for and join League 6
Qualify for and join League 5
Take a dog off your team
Qualify for and join League 4
Breed your first puppy
Expand your kennel
Qualify for and join League 3
Win a race against your rival
Qualify for and join League 2
Hire your first new dog