Here is the full list of all 16 THE 2048 achievements.
Reach 20K points in modern or classic 4x4 mode.
Reach 15K points in modern or classic 4x4 mode.
Reach 10K points in modern or classic 4x4 mode.
Survive 5 minutes in survival mode
Survive 1 minute in survival mode
Reach 1M points in any mode.
Reach 500K points in any mode.
Reach 300K points in any mode.
Reach 150K points in any mode.
Reach 100K points in any mode.
Reach 50K points in any mode.
Reach 30K points in any mode.
Reach 25K points in any mode.
Reach 5K points in modern or classic 4x4 mode.
Reach 3K points in modern or classic 4x4 mode.