They essentially are famous for a) buying bonds of states that are almost going to default and then court litigations with them for years until the state pays (Argentina is the most extreme example where they kept the bonds for 15 years doing court litigations with them, at some stage they even convinced Ghana to give to them an Argentinian navy ship, which was later overruled by some higher court), b) buying stakes at companies and forcing them to make changes and do whatever Elliot says, at times by doing literally blackmailing (in one case they found records from the divorce of the company’s CEO which amongst other things showed that he used physical abuse on his ex-wife and Elliot published them forcing the CEO to resign).
They are arguably the most feared hedge fund, and use the most extreme tactics to force states/companies do their bidding. Paul Singer (the founder) is also one of the biggest donors to GOP (around same level as Koch brothers and Robert Mercer).