During this run I completed the game with Kaname and the right conditions to obtain the Sesshomaru ending of the game. In this scenario Sesshomaru joins you for the battle against the large Hitogata boss and stays with you for the final battle with Naraku. In a way, beating Naraku with only Kaname and Sesshomaru is easier because Kaname can siphon hit points from Naraku and damage him each turn using the Chaotic flame attack and the fact that Sesshomaru is basically invincible.
To get this bonus ending you must go through the game and show favoritism to seshomaru only and keep interaction with the rest of the team at a minimum. This means that you will need to keep track of who you spend the mandatory “off” days with during the quest (It is possible to spread out the days so that you spend time with everyone once). Whenever possible you should always choose not to rest or stay when they give you a choice. You must also do the extra side quests (ones that appear on the over world as question marks) that consist of Sesshomaru and Rin. These are at the field of ignorance, where you will find a cut scene, and Pass to castle town.
In Minamo village you should choose to think about whoever is sick when Mahoro tries to trick you. When you destroy the crystal in naraku’s castle you need to go tell Sesshomaru about Rin instead of joining up with Inuyasha.
If all goes well and you limit personal time with your party you will see Sesshomarus image replace the other characters’ images when you save to a memory card slot. This means that you were successful and you have favored Sesshomaru the most and will get the bonus ending.