Successfully complete the “Deep In The Shadows” (second) main mission to unlock the “Finders, Keepers” side mission. Keep replaying the “Finders, Keepers” side mission to get a lot of Amrita. For even more Amrita, purchase the Amrita Blessing at the Shrine. Just ignore the other enemies and focus on the Kappa (turtle-like yokai with glowing shell). Kill the Kappa and collect the rewards. This side mission can be completed in about five minutes. Repeat this as many times as desired. You will get approximately 12k Amrita each time you complete the side mission, especially if you kill some of the enemies with the Amrita Blessing from the Shrine. This method also helps to quickly level up early in the game.
To get between 600k to 800k Amrita in ten minutes, first unlock the “Master Of The Twin Blades” side mission in the Omi (final) region. Successfully complete “The Way Of The Warrior” missions at the dojo to unlock “The Grimmest Blades” dojo mission. Complete “The Grimmest Blades” dojo mission to unlock the “Master Of The Twin Blades” side mission. Then, complete the final main mission and equip the Guardian Spirit you unlock to get a +12% Amrita drop bonus. Every time you complete the “Master Of The Twin Blades” side mission, you will get x2 “Saisetsu-shin’s Sake” items. These consumable items make it so your Amrita earnings multiply after each kill. The multiplier stops if you are killed. You can also join the Toyotomi Clan for an additional Amrita drop rate bonus. This method requires practice and preparation. The “Master Of The Twin Blades” side mission is challenging — so it helps to use twin blades or other fast weapons to kill opponents before you are completely overwhelmed. You have to fight Bosses and tough enemies, but a single run through the mission should only take 6-10 minutes, depending on your skill level. Defeating Nue is the hardest part of the mission. If you can complete the mission without dying, and use Saisetsu-shin’s Sake before the fight, you will get around 800k Amrita.
You get glory from fighting revenants (the red graves in missions that spawn the ghosts of dead players). You can farm it quickly by replaying low level missions where a lot of players have died.