You need to complete levels 1-20 of the Treasure Hunt challenge. These are point based challenges where you earn points based on combos. There are gems randomly placed on the board, and in each challenge you have a different set of chess pieces. You need to move your pieces such that they are attacking multiple gems of the same color at once. You earn more points when capturing more than 2 gems at once, and also if you can capture multiple colors at once (such as 2 green gems AND 2 red gems in the same move).
They are random, but you have unlimited tries. Focus on maximum gem combos and you shouldn't have any particular problems. Levels 17-20 are significantly more complex, but quite doable with a little patience. Look at every possible move before playing each turn, and calculate how many gems you will be able to get. If you select one of your pieces, every possible move is highlighted for you, which makes this much easier.