Here is the full list of all 41 Captures II achievements.
Complete Introduction.
Complete Trade Offer.
Complete Tile Effects.
Complete Tile Effects+
Complete Queen Mastery.
Complete Rook Mastery.
Complete Bishop Mastery.
Complete Knight Mastery.
Complete Challenge I.
Complete Challenge II.
Complete Challenge III.
Complete Challenge IV.
Complete Introduction using 2 or fewer perks.
Complete Trade Offer using 2 or fewer perks.
Complete Tile Effects using 2 or fewer perks.
Complete Tile Effects+ using 2 or fewer perks.
Complete Queen Mastery using 2 or fewer perks.
Complete Rook Mastery using 2 or fewer perks.
Complete Bishop Mastery using 2 or fewer perks.
Complete Knight Mastery using 2 or fewer perks.
Complete Challange I using 2 or fewer perks.
Complete Challenger II using 2 or fewer perks.
Complete Challenger III using 2 or fewer perks.
Complete Challenge IV using 2 or fewer perks.
Complete Introduction without using any perks.
Complete Trade Offer without using any perks.
Complete Tile Effects without using any perks.
Complete Tile Effects+ without using any perks.
Complete Queen Mastery without using any perks.
Complete Rook Mastery without using any perks.
Complete Bishop Mastery without using any perks.
Complete Knight Mastery without using any perks.
Complete Challenge I without using any perks.
Complete Challenge II without using any perks.
Complete Challenge III without using any perks.
Complete Challenge IV without using any perks.
Complete 5 trades.
Complete 15 trades.
Complete 30 trades.
Complete 75 trades.
Complete 150 trades.