Hold LB, LT, RB, RT then press B button to remove grid or press A to change jewel types.
To unlock Cognito Mode finish all the puzzles in Puzzle mode. It is okay to look at hints constantly to solve all the puzzles. Cognito Mode is basically Puzzle Mode with no hints.
Complete 280 levels of Endless mode.
Complete 8 levels in Action mode.
Complete 17 levels in Classic mode.
To play Bejewelled 2 with the same gameplay mechanics as Bejewelled 1 (asin the power gems and hyper cubes don't exist), go into Play Game when you first load up the game. Select the Classic, Action, Endless and Puzzle mode buttons (in that order) at the menu screen repetedly (so you're basically maneuvering the cursor across the screen clockwise). After several rounds, a window will come up saying 'Please Wait', and Original Mode will load up.
To get all the achievements in the game, do the following things: