Do it quickly, but carefully.

Literal

Swiftly, however with-attention do [command-なさい].

敏速に is the adverbial form of the na-adjective 敏速 ('swift, nimble'). しかし connects two contrasting instructions. 注意して is the te-form of 注意する used adverbially to modify やる. The paired but contradictory instructions make this a useful phrase for giving nuanced directions.