Originally Posted by
Ckaelir
The reputation and the Good Suramaritan are essentially connected requirements, being exalted isn't a requirement in itself.
To complete the Good Suramaritan achievement you need to be exalted (or 20,000/21,000 past revered, which is slightly before hitting exalted). However, you can start the Good Suramaritan quests early on, you need a certain amount of rep for each part to be unlocked and as you progress through the quests you'll gain some rep too.
Since your character is already almost revered, you can do most of the questline before needing to grind rep to unlock the last few parts.
I'm not sure if the rep you gain from doing the quests is enough to get you to exalted so be sure to do all the Suramar World Quests you find available (more will unlock as you progress through the story) and especially the Withered Training WQ (you need a certain score to gain maximum rep and it's easy now with the available gear, find a guide online).
Find a guide on how to increase your Ancient Mana cap as well since it's gonna help you out a lot and it's also a "hidden" requirement later on.
It's easy and a nice story too, just do all the Good Suramaritan quests and World quests you find, increase your Mana cap and always replenish it.
Keep in mind that if a character gets the Good Suramaritan achievement, you don't have to do it again on another character to unlock flying.