I've gotten both the Princess & Ferid on my first tries, it's really not that impossible... here's some simple strategies...
Checkers: Just pay attention, get up to the TV, map out all the possible moves that your opponent can make, and be aggressive. Playing defensive on this AI never works, it also tries to avoid Eye for an Eye (Sacrifice your piece to capture his piece) moves almost always, so use that to your advantage, and good luck!
Capture: Okay, this is VERY easy... here's a very simple strategy, take the left or right side piece, and move it up to about the 4th row... (counting from the bottom), and then just slowly build a wall, moving up, preventing the pieces around you from escaping into your territory, then just protect yourself on the sides, by slowly building in from your two side pieces, eventually, you'll make an uber-wall. In fact, the way I captured Ferid, was that I ended up capturing all of his pieces at once! It was awesome!
Territory: Okay, this game is really easy too... just stick a piece in the corner... left or right, doesn't matter, and eventually, when your oponent only needs 1 piece left, he'll start manuevering around his piece back and forth, wait until he gets to the other side of the board (move around another piece in a square pattern), and then your piece SHOULD be able to make it in 2 or 3 moves, this same thing can be done on Hard mode too, it's just a little tricky.