Information is definitely out-dated, and you shouldn't really take it to heart.
Achievements were like Badges, except they did not award you weapons or any items. They only award Cash/Coins, EXP and Fame, the three main ways of reward in-game. Some were re-doable while others are not.
The feature was new in R2DA, and was not in past Reason 2 Die games. This added a side objective to do in-game, though they didn't serve an important purpose.
When you received an achievement, it would appear in your mail, the main use of the mail system.
[Message]:Join your first game of Reason 2 Die Awakening and get a free gift.
Reward: 120$ Cash
[Broken Before Removal]: Get a friend to follow you in R2DA for the first time and get some free gifts.
Broken Reason: Universes; cannot follow a friend into R2DA for the first time without going through the choice universe.
[Scrapped]: Beat your old record on any Survival or Hard map to get a free gift!
Reward: 100$ Cash
Reason Removed: It is actually unknown why this was removed, but it is estimated that it was removed because you could easily reset every 1% to earn 100$ Cash, which would earn 10,000$ Cash per map and/or Gamemode.
Welcome to Reason 2 Die Awakening
[DEMO Only]: Claim your beginners REWARD by right clicking the letter icon and choosing delete.
Reward: 500 Coins
R2DA Opening Event
[DEMO Only]: This month we are happy to release R2DA out of demo. We celebrate this by giving out generous [sic]
- The Friendly Recruiter achievement could formally be easily exploited through the use of alternative accounts, and a couple of computers.
- This feature was removed in v0.9.6.
- This was technically in Debug for a lengthy period of time after removal, as in some servers, the mail system hasn't been removed yet.
- This was pretty much the only feature that used the mail system.
- During DEMO, the mail system was occasionally used for update logs such as the one here.