You've received some good advice so far, but I figured I'd throw my two cents in.
The first thing you have to consider is if your story is canon or not. If you're writing and AU then you'll have to think over what the character's archetype and alignment in canon is and then alter that towards your AU setting. I use an alignment system similar to role playing games (like Dungeon's and Dragons) which you can read more about
here. Archetypes are further discussed
here.
The second thing you have to consider is if your story follows the canon plot at all (even if your story is AU it may be a divergence which would still have to follow the canon plot up to a certain point) and at what point of the canon story you are following, then decide if the archetype and alignment you chose in step one is still accurate - if not, change it to what works best for that time.
The third thing you have to consider if character development. This is where it becomes easy to side down that slippery slope into OOCness. I'd like to point out that there is a massive amount of difference between true character development and outright OOC. Outright OOC is when you take a character directly from a certain point of the canon plot and then have them act blatantly against their alignment and archetype with no excusable explanation. (For example, Kagome suddenly hates InuYasha or Sesshomaru is magically a pacifist.) True character development would either follow the characters growing into the roles you need them to be in or provide some sort of logical explanation as to how they got there. (For example, a witch curses Kagome to hate InuYasha or Sesshomaru is a pacifist as a
child but grows into the less kind version of himself we all know later due to some sort of trauma.) If you are altering the timeline dramatically (Say you want to write a story that takes place in the distant future or past.) you will have to see if the archetype and alignment still matches what you need. If not, change it to what works best for that time.
Notice a pattern?
Character's archetypes and alignments grow and change just like people. We are not always once set way - we may be a certain way for a very long time, true, and some individuals are more set in their ways than others, but for the most part you can generally follow this to find where you need to be.
A Sesshomaru warrior archetype, chaotic neutral alignment is the typical of what we see of him in the canon story - but he
could be anything with the right development.
One thing to remember that may help is that when it comes to alignment you should follow it in an order like this:
Lawful Good ---> Neutral Good <---> Chaotic Good <---> Lawful Neutral <---> True Neutral <---> Chaotic Neutral <---> Lawful Evil <---> Neutral Evil <---> Chaotic Evil
Follow the arrows from the alignment that you feel best fits the character in canon and then go along the path towards the alignment you want the character to be in your story. If you pass any other alignments you must show a reason for development. For example:
Sesshomaru starts as a Chaotic Neutral Warrior but I want him to be a Neutral Good Mentor in the modern world. Following that pattern I must show:
1. How Sesshomaru went from being a warrior to a mentor. (Perhaps he chose to change roles out of necessity as humans began to take over Japan.)
2. How Sesshomaru went from Chaotic Neutral to True Neutral. (Perhaps after Naraku's defeat he feels a sense of ennui as there is no one in Japan who poses a real threat to him anymore.)
3. How Sesshomaru went from True Neutral to Lawful Neutral. (As his warrior ways begin to lose value, he starts to become more of a leader in order to protect his pack/other youkai/himself.)
4. How Sesshomaru went from Lawful Neutral to Chaotic Good. (Humans can be really stupid and Sesshomaru disdains their governments, particularly after the bombing of Hiroshima and Nagasaki. He chooses to act in order to bend favor towards balancing things in a way that he feels would be better for Japan.)
5. How Sesshomaru went from Chaotic Good to Neutral Good. (Time goes on and with technological advancements and more stability among humans, Sesshomaru sees no reason to be so aggressive in his actions and stands back to guide those who now act.)
You don't have to describe
every little thing but you do have to show the change in some way, even a sentence or two can often explain things to your readers. No matter what, however, changes you make should make sense for the time period, the archetype of the character, and their alignment. Everything else... is up to you.