Battle vs. Chess

This has to be done against the AI. The easiest way to do this is to play against a difficulty 0 AI and capture most of his pieces. At that point, use five different pieces to put his king in check and the achievement will pop. Note that this does not have to be done with five different types of pieces, you could in theory do it with five rooks (assuming you promoted three pawns to rooks and as such HAD five rooks).