Here is the full list of all 38 All I Want for Christmas are Subgames achievements.
Complete Click to Swap Layered Mode
Complete Click to Place Mode
Complete Word Search Mode
Complete Connect Mode
Complete Swap Mode
Complete Shapetris Mode
Complete Phrase Letter Swap Mode
Complete Paint Mode
Complete Montage Mode
Complete Memory Mode
Complete Jigsaw Mode
Complete Hidden Object Mode
Complete Find the Difference Mode
Complete Detail Mode
Complete Click to Cycle Mode
Complete Click to Swap & Rotate Mode
Complete Crossword Mode
Complete Collage Mode
Complete Color by Pixel Mode
Play a Click to Place Mode without using Hint
Play a Word Search Mode without using Hint
Play a Connect Mode without using Hint
Play a Swap Mode without using Hint
Play a Shapetris Mode without using Hint
Play a Phrase Letter Swap Mode without using Hint
Play a Paint Mode without using Hint
Play a Montage Mode without using Hint
Play a Memory Mode without using Hint
Play a Click to Swap Layered Mode without using Hint
Play a Jigsaw Mode without using Hint
Play a Hidden Object Mode without using Hint
Play a Find the Difference Mode without using Hint
Play a Detail Mode without using Hint
Play a Click to Cycle Mode without using Hint
Play a Click to Swap & Rotate Mode without using Hint
Play a Crossword Mode without using Hint
Play a Collage Mode without using Hint
Play a Color by Pixel Mode without using Hint