Once you have done something, or reached something, you will get an achievement. You can't get achievements during havoc. There are 32 achievements that you could get, achievements are one time things. Each time you get a new achievement, you will receive 50 blue tokens.
You can see your achievements under the achievements tab in your profile.
Achievements at any time
You can get these achievements at any time in the round, regardless of the tick.
Achievements after tick 500
You can only get these achievements after tick 500.
Achievements at the end of an era
You can only get these achievements at the very end of the round, before the world goes into havoc.