On the main menu screen, you can receive a gold medal next to each mode's button. To get the medal, you must complete each puzzle in that mode in under an hour (each solution must be displayed in color at the end).
Special Puzzles
By having save data from the previous three Picross e titles on your 3DS, you can unlock five special puzzles. They appear as a gift icon next to the "Mega Picross" option.