I'd suggest looking at the general Facebook achievements API: https://developers.facebook.com/docs/games/achievements/
Also you can first test out what to actually put with the graph explorer then put that into graph.: https://developers.facebook.com/tools/explorer
So for example to create a new achivement it's just this:
var dict = new Dictionary<string,string>();
dict["achievement"] = "<URL_TO ACHIEVEMENT_HERE>";
FB.API(FB.AppId+"/achievements", Facebook.HttpMethod.POST, null, dict);
To get all your game achievements, it's:
FB.API(FB.AppId+"/achievements", Facebook.HttpMethod.GET);
Then to award a player an achievement, it's just this:
var dict = new Dictionary<string,string>();
dict["achievement"] = "<URL_TO ACHIEVEMENT_HERE>";
FB.API(FB.UserId+"/achievements", Facebook.HttpMethod.POST, null, dict);
To get that player's achievment that they completed, it's:
FB.API(FB.UserId+"/achievements", Facebook.HttpMethod.GET);