The achievement Ben-Hur is a reference to the titular character from the novel Ben-Hur: A Tale of the Christ who wins a chariot race against his former-friend turned bitter rival in the book's climax.
The achievement Circle of Life seems to reference the song by the same name in Disney's 1994 movie, The Lion King. This is further supported by the fact that the icon is heavily reminiscent of Pride Rock, the location of the lions' den in the film.
The achievement Elementary, Dear Bayek is a reference to a catchphrase allegedly said by the fictitious detective Sherlock Holmes to his assistant, Dr. Watson, but the line was never written in any of Sir Arthur Conan Doyle's works and is instead a popular misquotation.
The achievement You still need 8880... is a reference to the "It's Over 9000!" meme derived from a line uttered by the Dragon Ball Z character Vegeta regarding personal power levels.