I have been soundly defeating Little Chess Partner on its strongest setting with so much predictability that there are many lines I have calculated out to a forced mate. Significantly, this is when I am White and play 1. e4. There is a line in the Advanced Varation of the Caro-Kann, for example, where I force mate in twenty moves, and in the Winawer French the computer accepts a sacrifice out of the opening that results in White queening a pawn by force. Because the computer tends to endlessly repeat the same absurd mistakes, the situation can become ludicrous. Like many computers that are not really super- strong, Little Chess Partner tends to be too materialistic. It will often grab a pawn when it is virtually suicide to do so, but this affords the human player a chance to pratice executing the resulting positions to a win. I don't like generalizations in chess because  each position is unique, but if you try sharp lines, point your Bishops at the Kingside and then storm it with pawns, believe me, you will start beating Little Chess Partner much more frequently. I've also noticed that whenever I'm able to pry open the h-file I get a crushing attack and win almost every time.  My best results come when as White I play e4 and then steer the games into Closed Sicilian-King's Indian Attack-type openings.

I have won against Little ChessPartner set to Hard level a few times, although it has beaten me more times than I have beaten it.

I don't think there is a secret with this program as it is fairly strong, you just have to play a very tight game especially when black and try and stay level on pieces as much as possible.