Achievements are fun. Most gamers will agree with that statement. They provide a nice sense of accomplishment when you, well, achieve them. It is quite rare that they have an actual impact on the game, but they are fun goals to shoot for nevertheless.
However, several games have taken achievements to the next level. Halo 3 grants cosmetic armor permutations for completing tasks, Mass Effect gives minor bonuses to stats and abilities for your efforts, and Team Fortress 2 allows you to unlock special weapons for achieving goals. In these games, achievements are more than just nifty little milestones. They directly impact the gaming experience in a positive manner.
This mechanic should be introduced to Demigod. Currently, there is a small Favor Point bonus for getting achievements. Especially with the current Favor Item pricing, this is rather insignificant. They provide a nice little boost to get you started, but when it comes down to it, there is no reason to really try for a specific achievement. Anything you gain could also be gained by playing a few quick matches. Without even being linked to a universal GamerScore like Xbox, there is little to no reason to try for achievements.
Thus, I propose Achievement Items. Perhaps in addition to the current Favor Point boost you get from getting achievements, specific items should be rewarded to people who put forth the effort. These Achievement Items would essentially be Favor Items that are unlocked through a different manner (would take up the same slot, would be used in the same way, etc...). Instead of saving up Favor and buying them, you would unlock them from completing specific achievements and/or a percentage of achievements for a specific Demigod.
One benefit of this is that it allows new and interesting achievements to be added. Honestly, the current achievements are fairly bland. They mostly consist of "do such and such this many times total", or “do such and such this many times in a single game". With specific goals and rewards, you could introduce achievements like "Hit all 5 opposing Demigods with a single Hammer Slam" for the Rook or "Win a match without getting hit" for Regulus. Those are perhaps on the more difficult end of the achievement spectrum *coughtwoforonecough*but you get the idea. If there is a reason to achieve, then achievements become more than random requirements for fake awesomeness.
Additionally, the Achievement Items themselves could vary greatly. With specific requirements to get (unlike random Favor amounts), the Items could reflect the challenge that it took to get them. For example, the Hammer Slam Achievement Item could reduce Hammer Slam's casting time by 25%.
Finally, this would be great content for expansions. Just look at TF2. Their expansions consist of a new map and the next achievement pack, which leads to new weapons and gameplay. I think this would be an excellent element for Demigod's expansions. In addition to adding a new Demigod and map, an achievement pack could be added for an old Demigod (or new achievements could be scattered among the old Demigods) to encourage people to revisit them in addition to all the new material. It would be a little thing that increases the longevity of the game for casual passer-bys as well as a way to open up whole new strategic options and builds for seasoned players.