There are two extra, hidden stages you can play in each zone. To play one of the hidden stages (appended with the phrase "-06"), you need to get an A-Rank score or better on the other levels of that zone. To play the other hidden stage (appended with "-05"), you must get an S-Rank score on the other levels of that zone. Zone 11 is excluded from these conditions, however, as its stages are unlocked as you play and beat the game.
Extra Zones
By completing the game (the final level being Zone 10-04), you will unlock two new, special zones for you to play. Zone 12 is special in that the speed in there is around 50% faster than usual, which makes matching Pokemon harder as you have to go much faster. Zone 13 will also be unlocked; it is a zone where the levels are endless and your main reason for being there is to get a high score. (Note, however, that Zone 13 still allows you to successfully Trozei Pokemon you've yet to Trozei.)
Zone 11 - Safari Jungle
The Safari Jungle is a unique area in the game that contains different Pokemon in each of its three stages on different days - you won't find the same Pokemon on Monday that you did on Sunday, for example, but the Pokemon on Monday in the same stage are always the same. (Pokemon Battle Trozei uses the Nintendo 3DS calendar to determine the day, by the way.) You will unlock a new stage in this Zone by completing Zone 3, another by finishing Zone 6, and the final stage by completing the game, with the difficulty in each stage increasing also.