Achievements can be a great way to track personal progress, and see how much you have progressed. Furthermore, I think it would be a pretty good motivating factor towards practicing Competitive Programming more.
General outline of achievement tab on user profile
Achievement examples:
[Achievement] + [date obtained]: Reaching Specialist!
[Achievement] + [date obtained]: Reaching Expert!
[Achievement] + [date obtained]: Logging on Codeforces daily for a year!
[Achievement] + [date obtained]: Top 1000 in a Div 2. Contest!
[Achievement] + [date obtained]: Fullsolved a Div 2. Contest!
These are just some rough ideas for achievement functionality.
Conclusion
This is just my suggestion towards an achievement system, so it is probably flawed in a lot of areas, but I just wanted to pitch in my ideas to the community!
Feel free to comment any additions to this idea/flaws about this idea. I am open to any criticism about this.