Tough blighter regarding US city accepting source of corrupt cash (4,8)
I believe the answer is:
hard currency
'cash' is the definition.
(thesaurus)
'tough blighter regarding' is the wordplay.
'tough' becomes 'hard' ('hard' can be a synonym of 'tough').
'blighter regarding' becomes 'currency' (I can't explain this - if you can you should give a lot more credence to this answer).
'hard'+'currency'='HARD CURRENCY'
'us city accepting source of corrupt' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Other definitions for hard currency that I've seen before include "Very stable means of exchange" , "Money in demand from foreigners" .)