Please note that as long as a card has not been completed by you, Card Pieces can be stolen by other players via battle.
The Card Piece collection system is competitive by design. Whenever you attack another player for a Card Piece and win, he will also lose his Card Piece.
More attractive Card Pieces such as Legendaries are subject to a lot of fights and successfully completing them is part of the challenge.
When you want to fight for Card Pieces, go to the Arena, select Card Pieces, and attack another player. If you win, you will be rewarded with his Card Piece.