To complete Cerberus' favor, he must be pet at least 20 times. (Pets given before the final favor lock was added to the game are not counted, so fortunately you must pet him another 20 times)
Petting him 10 times earns the Three-Headed Boy achievement, which is an indicator that you're at least halfway there.
'...The fearsome multi-headed hound of hell is really not so bad as his deserved reputation otherwise would lead you to believe. Yes, the massive beast has feasted on no short supply of interlopers to the Underworld, or on those attempting to escape. However, tales of the number of his heads are oft exaggerated, and in his old age, his temperament has grown much more relaxed. Indeed, he seems one of the sole sources of comfort for the House's grim Master. The fact that Cerberus now frequently rests at his Master's side also suggests the Underworld has new vulnerabilities, a source of some concern to the Lord Hades, who understandably takes pride in his domain's imposing reputation.'
Cerberus Bond Forged Icon
For additional information on Cerberus that does not pertain to Hades, see Wikipedia's article: Cerberus