Bitcoin and other cryptocurrencies undoubtedly offer new opportunities for financial transactions. However, they can also be used for purposes of financial crime, such as fraud and money laundering. The absence of central control and the pseudonymous nature of transactions make cryptocurrencies appealing for illicit activities.
This is also describing cash/fiat. What do you think can be done to mitigate the risk of cryptocurrencies being used for criminal purposes? What measures should be taken? 
Nothing. It will be lessened dramatically over time when most people that are into it are using it as an asset or store of value. That will come naturally when the majority of the people are into it but just as the usage of cash is done with several illegal uses. Bitcoin will be attached on it for as long as it can.