I'm a Levelord - I reached Level 10 in Classic Mode!
It is possible to run out of matches in Classic mode! Look out for ways to create special gems and hypercubes. They can save your live! Save them for emergencies instead of wasting them. The board will get mixed after each completed level but you will keep your special gems. My strategy is to work my way up from the bottom because you will always get new gems at the top. Another way is to start either on the right or left side. It is not good to match random gems without thinking. Use the hint button if you get stuck and take your time. You can't run out of time in this mode so take it easy. You can always use the TerreDactyl-method if you can't do it legit which will make this achievement a cakewalk! Quit to the main menu after each level and copy the save file ("C:/users/[yourusernamehere]/Appdata/local/packages/PopCap.BejweledLIVE_dw446q17t8sdy/local state/classic.sav") to the desktop and try other matches if you fail.