Here is the full list of all 12 Mystic Journey: Tri Peaks Solitaire achievements.
You need to remove a card that chains cards of the same color so that, as a result, not even one chained card will appear.
In the Tropics, complete 7 levels within one day.
In the Volcano, complete 7 levels within one day.
In the Valley, complete 7 levels within one day.
Win 5 times without losing.
Remove 5 cards in less than 5 seconds.
Make a chain of 15 cards.
Complete any 10 levels gaining all three stars.
Remove a card with timer not later than in 2 seconds before an explosion.
Complete a level in 30 seconds.
In the Mysterious Forest, complete 7 levels within one day.
In the Floating Islands complete 7 levels within one day.