How do you unlock Supergirl in lego batman 2?

You can't unlock Supergirl in Lego Batman 2: DC Super Heroes. She is not a playable character in that game.

Supergirl appears in the game as a non-playable character during certain story missions and cutscenes. She is also featured in some of the collectible story-related items.

However, she is a playable character in later Lego games like Lego Batman 3: Beyond Gotham and Lego Dimensions.