IIRC there was some fighting, but in the end the Danish plans just quietly came to naught. Hamburg traditionally ran a policy of carefully balancing between the counts of Hostein, the emperor, and the Danish king, occasionally claiming to be subject to either, but always striving to maintain as much freedom of independent action as possible. It was also a very heavbily fortified town with extensive landholdings at the time, so a siege could have become quite costly.
In this particular case, Hamburg had been laying claim to the status of imperial free city since the beginning of the century, a claim that the Danish kings did not recognise. It seems that a faction inside the city asked the Danish king to support them against a local rival, Celle, but the king's demands were such that the citizens came to support the other party, allied with Celle and closed the doors on him. There was an attack in 1686, but as I said, Hamburg was quite heavily fortified. No real siege was attempted, it seems.