自分たちだけで is used with the meaning of "all by yourselves".
自分で is often used in situations where you would use a reflexive pronoun in English, for example
自分でできた
I managed (to do it) by myself / She managed (to do it) by herself / etc.
where the translation of course depends on the context.
In 自分たちだけで
- たち is added to make it plural (ourselves, yourselves, themselves) and
- だけ "only" to emphasize that whatever they did, they did without any external help — in English 自分だけで could be translated as "all by myself/herself/..." for emphasis.