Skill and proficiency are key. For example, an assassin like Agent 47 from the 'Hitman' series is highly skilled in using a wide variety of weapons, disguises, and stealth tactics. This allows him to infiltrate any situation and eliminate his targets without being detected.
The ability to outwit opponents is crucial. In the case of Arya Stark from 'A Song of Ice and Fire' series (and the 'Game of Thrones' TV show), she is constantly evolving and learning new skills. She uses her wits to get close to her targets and then uses her training in combat and assassination techniques to achieve her goals. Her ability to blend in, whether it's as a boy or in other disguises, and her sharp mind make her a great fictional assassin.
A great backstory can also contribute. Take Alucard from 'Hellsing'. His vampire nature gives him superhuman abilities, but his complex history of serving the Hellsing Organization and his battles against other supernatural beings add depth to his character as an assassin. He is not just a killing machine but has a purpose and a code that he follows, which makes him stand out as one of the best in fiction.