There are a total of 9 Covenants you can join and gain ranks in. Each of them have 3 ranks, and require some sort of offering or action to rank up in. The list of Covenants and requirements is as follows:
(Covenant) - (Offering or event). (Amount for Rank 1, 2, and 3, in that order).
Way of the Blue - Kill invading phantoms. 1, 5, 10.
Company of Champions - Offer Awestones. 10, 25, 50.
Blue Sentinels - Offer Tokens of Fidelity. 50, 150, 500.
Bell Keeper - Kill Belfry Invaders. 10, 30, 100.
Brotherhood of Blood - Offer Tokens of Spite. 50, 150, 500.
Heirs to the Sun - Offer Sunlight Medals. 10, 20 ,30.
Rat King - Offer Rat Tails. 10, 20, 30.
Dragon Remnants - Offer Dragon Scales. 10, 20, 30.
Pilgrims of Dark.
Now obviously the Blue Sentinels and Brotherhood of Blood are completely out, as they have insanely high requirements, according to the guide. No one I've seen has been able to actually confirm how to rank up in those. Company of Champions also makes the entire game harder for the player, so that's probably not a good choice either.
All of the rest are rather easy all around. Bell Keeper is good for anyone who likes PvP and should be self-explanatory once you find the covenant at the beginning of each belfry, Way of the Blue will have you waiting for someone to invade you, either player or NPC invader, and Heirs of the Sun are good for people who like to co-op bosses, and is probably the easiest covenant for anyone with an internet connection and Xbox Live.
Heirs of the Sun
However, for people who play offline, and the people who simply don't want to play with others, there is a much better, single-player choice: Pilgrims of Dark. This Covenant requires no offerings to rank up, and instead, you must meet Darkdiver Grandahl in three locations around the world and progress in his questline to reach the full rank. The locations are as follows:
- Behind the door in Black Gulch opened with the Forgotten Key, which can be found in a cave below the door by killing the two Elite Giants.
- After dropping through the false floors in the Shaded Ruins.
- Behind the soul-activated door in the far left corner of the large room next to the King's Gate Bonfire in Drangleic Castle.
Meet him at those three places, and then he'll allow you access into the Dark Chasm of Old, which you need to go into at each of the three places you met him (by offering Human Effigies), clear the areas within, light the torch in each, and then defeat the Darklurker boss. The achievement should unlock after this whole questline.
Also, I should probably add from personal experience: the Dark Chasm of Old SUCKS. If you're not a faith or caster build, you probably shouldn't attempt it. I managed to get through each of the areas as a melee build, but I had to use a soul vessel to respec to a faith build to defeat the Darklurker.