Nimble Gardener - you have to choose expedition side on Eden or do this achievement throw the main quest in the beginning of Eden. There is expedition daily and main quest where you have to kill 10 fingus/plants(don't know their name). To get this achievement you need to catch 10 seeds that those plants are throwing(don't kill plants before getting achievement). Plants from eastern base Penelopa don't have an ability to throw seeds and you can't get this achievement from them.
Phew! - While Eden battle you have to bring seed to the point having low hp. Didn't test actual number, others say it has to be less then 10-15%.
Exile - You have to eat an apple on Eden. Apple can be found during main quest on Eden branches when you come on Allmother's judgement, there is Serpent on the beginning of the needed branch and apple tree is at the end of branch. If you already completed this quest you can find this tree in allmother's "home" to the left from her(added in 13.1). This achievement was broken on ru servers for about 5-6 months, you couldn't use apple tree on eden branches and there was no apple tree in allmother's "home".
Auras are some new feature which we still don't have, there is still no way to get new ExoMount skins(announced in may).. Maybe they will be added in 14.0..