Introductions can be earned by starting the arena in scenario campaign or by beginning arcade mode with each character. Endings can be earned by completing these modes, or by using the method below.
Spoiler alert, this is a guide primarily directed towards owners of a turbo controller. From messing around just a bit on a secondary account I have realized that if you simply turbo the X button upon starting a mission, you can keep resuming it and gradually unlock the endings this way. Every few failures you will see a message pop up that the ending was unlocked for a random character upon the start of the retry.
This being said, it saves you the hassle of arcade/arena playthroughs for each character. If you do not have a turbo, you could still do this only you'd have to watch the screen and simply click retry if that were easier though I personally would just rather play through as it would become rather boring.
Make sure you have nothing but default gear on both your primary character as well as your partner. Personally I allowed the game to run on Nightmare Train on hard and that gave me some quick failures. Once it starts up, just turbo X and you can leave the PS3 running knowing that you're gradually earning endings and not having to face Azazel.
There were a couple things I found when trying this again, however. At first the game would not give me any endings despite me failing multiple times in a row. I'm not sure about this, but I believe I had to complete and arcade run before attempting to earn the endings this way. It may seem stupid but it hadn't worked until I did this, perhaps the game wants you to at least earn one ending before getting it the easy way?
Also, if you want quick losses and don't have a turbo nor do you feel like waiting simply boot up the stage with Anna or any other stage that starts you near a ledge and jump off by pressing back and up near the ledge. Doing this will take a bit longer and quite a bit more effort, but it's still easier than the arena.