Here is the full list of all 34 Stars, Stripes, and Subgames achievements.
Play a Click to Swap Mode without using Hint
Use Hint for the first time
Complete Collage Mode
Play a Word Search Mode without using Hint
Play a Memory Mode without using Hint
Play a Slider Mode without using Hint
Play a Click to Cycle Mode without using Hint
Play a Paint Mode without using Hint
Play a Jigsaw Mode without using Hint
Play a Click to Rotate Mode without using Hint
Play a Click to Swap & Rotate Mode without using Hint
Play a Word Guess mode without using Hint
Play a Crossword Mode without using Hint
Play a Shapetris Mode without using Hint
Play a Collage Mode without using Hint
Complete Click to Swap & Rotate Mode
Complete Click to Cycle Mode
Complete Click to Rotate Mode
Complete Click to Swap Mode
Complete Sort Mode
Complete Find the Difference Mode
Complete Jigsaw Mode
Complete Memory Mode
Complete Paint Mode
Complete Slider Mode
Complete Shapetris Mode
Complete Phrase Letter Swap Mode
Complete Word Search Mode
Complete Crossword Mode
Complete Word Guess Mode
Play a Sort Mode without using Hint
Play a Find the Difference Mode without using Hint
Play a Phrase Letter Swap Mode without using Hint
Use Hint at least 10 times