These are the trophies and conditions as outlined when they were being introduced. I don't know if they have undergone any changes since then. These were a Purch thing.
1. First Message; Post your first message
2. Somebody Likes You; Your first like
3. Infant; Active member for 2 months
4. Contributor; 100 messages posted
5. Lurker; 2 month old member with 0 posts.
6. Scout1; Earn 20 Trophy Points
7. Explorer; You arrived on this site from a search engine
8. Ambassador; Associated your forum account with Facebook, Twitter, and Google
9. I Like It A Lot ; You've received 25 likes.
10. Aren't you precious?; You've received 100 likes
11. Elder; 2 years on AT forums
12. Ancient; 4 years or more on AT Forums
13. 16 Candles; Have a message to likes ratio of .2
14. Cipher; You enabled Two Factor Security
15. Wow, what a cache! - Your content has been liked 250 times.