Each Zone contains two bonuses stages that can be unlocked. The 05 stage becomes available after an "S" rank is earned on all other stages of that zone. The 06 stage becomes available after an "A" or better rank is earned on all other stages of that zone. Note: This has no effect in Zone 11.
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.)
Accessible from the title screen via the middle option on the bottom, the Play Data Card is mostly used to keep track of certain records in the game. However, as you bypass certain milestones, you will get the statistics highlighted and a crown placed next to them, and then the card will also change color with every two crowns you gather. The approximated milestones are below
Complete the indicated task to unlock the corresponding Pokemon.
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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.
Complete Zone 3.
Complete Zone 10-04. This zone features 50% faster speed.
Defeat Darkai (Stage 4) with a single hit.