だけは

だけは singles out one thing as holding true, or as the least that is done, whatever happens to everything else: "at least", "if nothing else". It follows a noun directly, and the は sets that one thing against the rest.

Doing as much as you could

With the same verb twice, dictionary form before だけは and た-form after, the action was done as fully as possible, but the outcome is uncertain or disappointing. The second half often says so.

The second verb can also be a request or a suggestion: たのむ頼むだけはたのんで頼んでみよう。

"Just not that"

With a request or a negative, だけは picks out the one thing that must or must not happen, while everything else is open.