Important to note that this raid was approved by Trump appointees so can not be a witch hunt.
The probable cause apparently was found by Mueller's team who then consulted with Trump appointed senior members at the DOJ who agreed it should be passed onto the FBI in New York.
FBI NY would confer with the highly respected Southern District of NY (SDNY) DA office. The Trump appointed SDNY DA must have signed off on an application to a judge. The judge must have concluded that there was probable cause a crime had been committed. The fact that it is a lawyer's office raises the standard even further. Cohen's office is in Trump Tower and his only client is Trump so this likely relates to Trump. Solicitor-client privilege does not apply to communications in furtherance of a crime-fraud.
My understanding is that one of the investigations relates to bank fraud. I am going to guess that he did not obtain his line of credit by telling the Bank he wanted to use the money to pay off a porn star.
Another investigation relates to a election finance violation so my guess would be an illegal contribution by the payment. Any communications with Trump about these issues may fit within the crime-fraud exception and may possibly be used to indict/impeach Trump.
But who knows. This guy is slippery as fuck for some reason. I doubt his base cares and the GOP may not either.
p. s. > Mr. Cohen began his career as a personal injury lawyer and taxi fleet manager.