They do their best to interfere with their fishing practices, following them around and pulling up their illegal nets, and sending their location to Interpol.
It's likely that whatever remaining shred of legitimacy such operations have is highly dependent on not having high-def video of their operations on TV and the internet as well.
As the article states, what they do that is most harmful to them is to follow them around and notify any port they attempt to dock at, so they can't get supplies (esp fuel) without risking arrest.
Honsestly, if this is something you are interested in, you should read the article. It's quite good and covers all the details of how the ship is wanted by Interpol and where these activists get the legal authority for what they do out there.
The Sea Shepherds were cutting their illegal nets and taking their buoys, and were reporting them to the local authorities whenever they approached a harbor. The fishing boat had no way of selling its catch or taking on more supplies without first losing the Sea Shepherds tailing them.
