On the Offensive is an accumulative meta-achievement which is completed during Covenant assaults in the Maw. It is a requirement to purchase the final mount tint from Death’s Advance quartermaster in Korthia. Thanks to the nerfs, you now need to complete only 6 random achievements out of total 9, and it’s properly account-wide – that means, you have to do it only on one character to purchase mounts on other Covenant alts (or after swapping a Covenant).
Achievements vary in requirements, but could be roughly split in two categories: the ones where you need several assaults and the ones which you can complete in one sit. Good news: for the majority, you don’t have complete a whole assault, or in some cases – even the associated quest.
United Front – is the easiest achievement, you require 2 weeks to complete it. Just run through every Covenant’s assault till the end – Kyrian, Necrolord, Fae and Venthyr – and check.
Other achievements are divided by 2 per Covenant.
A Sly Fox – is not quest associated. Talk to Orator Kloe to get a buff and track a fox. You need three Kyrian assaults to track it three times – so it does not depend on random, but stretched in time and cannot be completed during single assault. You get a pet as a reward for the achievement. Personally, I do not recommend it for length and bugs.
The Zovaal Shuffle – requires the quest The Ember Count. You need to talk to Gubbins to get a parasol (the thing you would be doing anyways to do the quest), hug a forge that spits flames and type a /dance emotion. Highly recommended, as after farming souls for half a year you perfectly know where all forges are, it’s quick and super easy to complete. Dance right in the forge, and don’t interrupt dance until you get the credit, rinse, proceed to the next forge.
Krrprripripkraak’s Heroes – requires a quest Just Don’t Ask Me to Spell It. You mount a tirnenn (the tree person) and toss animals to damage foes and help allies. Highly recommended, as you can do the achievement in the course of 10 minutes. Find all the required NPCs and help them (they have a debuff which explains upon hover on which ability to use). If any of the NPCs are not found at their spots, you may reset quest and try again.
Jailer’s Personal Stash – completed during A Shady Place quest. Enter the shadow world, and you find chests there. 6 chests are available daily. You may also reach them via repaired riftkey in Korthia, but the path is long and full of horrors, so I would not bother. Consider this an accumulative achievement.
This Army – requires You and What Army quest. You need to pick each of the five minions, with 3 up at the same time. As of October 2021, you may complete any other assault quest with a minion which counts into achievement, abandon What Army quest, and pick another one for the next assault quest. Chamipons reset daily, so you may do 4/5 per one assault – because there are 4 quests in one assault.
Up for Grabs – an accumulative achievement. As the name suggests, you find the required caches up the ramparts of Perdition Hold. By design, you need Putting a Plan Together quest which allows to mount an Overcharged Centurion and hop up, but you can also use a grappling hook if you earned it during Ven’ari questing and activities before. Some of the caches don’t count randomly into achievement, mount or no mount, and few are available daily, so achievement is generally not recommended.
Hoarder of Torghast – requires a quest Fangcrack’s Fan Club. Simply wait in the quest area as Fangcrack will pull anima powers and phylacteries out of portal, and grab/destroy them. Could be done in one sit, I spent no more than 10 minutes on it, so highly recommended.
Tea for the Troubled – requires A Tea for Every Occasion quest. You need to serve tea to the named NPCs, not the common ally mobs. A total of 8 and a daily rotation, technically could be done during one assault, just don’t finish this quest on day one.
As you see, the requirements for all achievements are quite reasonable, not tricky and are not something that should be shunned forever. Given the random appearance of the quests, the best tip would be to arrive at an assault spot, see if the listed quests are up, do as many requirements as possible per assault/per quest, and see which achievements come to finish first. Given the random nature of quest rotation, the most tedious quest could appear your best shot in the long run, so aim for all of them.
There’s zero competition from other players, so I would advise doing them on high hours, upon reset time. Other players would destroy the meddling mawsworn mobs during their own questing, so you could walk relatively safely in quest areas.