so the repl.it achievements is a new feature of this summer. basically, you get those achievements badges for doing stuff like coding every day, posting on repl talk, or answering other peoples' questions.
i dont think those achievemnets have any use (like cycles) but they are a way to encourage users to be more productive/active on repl.it
read more about it here: https://docs.repl.it/misc/achievements
Happy coding! =)