Order of Endings in NG for Sekiro

I had the same question when I was getting the Platinum Trophy. I found that the easiest way to get all the endings (in the same save) is by following this order:

• Purification (hardest because you need to beat Owl (Father)). I also recommend you to beat the Demon of Hatred in your first new game [NG].
• Return [NG+].
• Immortal Severance [NG+1].
• Shura [NG+2].

There is a very nice guide to obtain each ending in this link.

Starting on NG+, you may hit the wall with some bosses. If that happens, I strongly recommend you to practice using the Free DLC Reflections of Strength. In my case, I need to practice dozens of times the fight with Isshin, The Sword Saint before I was able to defeat it successfully in NG+ and beyond.