Team Fortress 2 has lots and lots of achievements. Most of them require you to do some pretty specific things, and often with the assistance of other players, but there are a few that don't.

For these, you could create a new server, set a password that you don't tell anyone, and then play the game solo.

And, as long as you met the requirements, you'd start getting achievements!

Though, there are relatively few you can do this way, so you won't make much progress until you start playing with Real People(tm).