Here is the full list of all 10 Solitaire achievements.
Win 5 games of FreeCell Solitaire
Win one game each of all 3 kinds of solitaires
Win 5 games of Klondike Solitaire
Win a game of Klondike Solitaire
Win a game of Klondike Solitaire without using undo
Win a game of Spider Solitaire in beginner level
Win a game of Spider Solitaire in intermediate level
Win a game of Spider Solitaire in advance level
Win a game of FreeCell Solitaire
Win a game of FreeCell Solitaire without using undo