The Atlas rushing strategy is one of the most consistent farming strategies that works well from the beginning to the end of a league. It is also one of the strategies that do not require you to have increased item rarity on gear.
The general idea is that you speed through maps as quickly as possible, more or less ignore everything except the boss, to reach the important maps listed below.
Breachlord Sacs are guaranteed drops from the boss fight in the Hive colony. This boss can also drops some lineage supports and unique items that might be worth a few divines as well. To access the boss fight you need to find a breach area in the atlas, with a breachstone in your inventory you can discover the area. Path directly to the Hive colony and kill the bosses in there for a guaranteed Breachlord Sac.
Audience With The King
If you have an Audience With The King in your inventory while browsing the atlas, you may come across the option to reveal The Crux of Nothingess. This reveals a map area where you can fight The King in The Mists. This boss is guaranteed to drop a Head of the King which usually is worth over a divine. You also have a chance to drop Ingenuity and From Nothing which if well rolled can sell for a lot of divines.
Jade Isle and Sacred Reservoir (Lineage gem map bosses)
Currently there are two maps we are looking for here, Jade Isle and Sacred Reservoir, which have a small chance to drop Rakiata's Flow and Garukhan's Resolve respectively which are worth a ton of divines. You won't be able to run the map until you complete some of the surrounding maps.
Before you run the maps, make sure you have Memories of the Karui and Memories of the Maraketh unlocked on your atlas tree and also use Jado with Untold Histories to increase the chance of dropping a valuable lineage support. It might also be worth to use Forest Mastery: Lineage Gems in your Atlas together with a Mastered Domain Irradiated Tablet with the modifier "Map also counts as a Forest Map". It is also believed that having a waystone and tablets with high waystone drop chance increases the chance to drop lineage supports very slightly, however this is not confirmed. With that said the chance to drop one of the good lineage support is probably less than 10% for a map, so take that into consideration before investing too much on these maps.
Hidden Jade Isle
Hidden Sacred Reservoir
The Tamings
You can create a The Taming by combining Berek's Grip, Berek's Pass and Berek's Respite at the secret room at the start of an Azmerian Ranges map. The Taming usually sells for many divines more than the three Berek rings would cost you.
Immured Fury
The Immured Fury boss fight has a guaranteed Fracturing Orb drop which usually goes for many divines. In order to encounter this boss fight you need cleanse a corrupted area by defeating the corruption boss in the corrupted area with a glowing red outliner like in the image below. When you reach this map and kill the regular map boss, the corruption boss will spawn shortly after.
If you are lucky, one of the cleansed areas will have an Immured Fury boss fight, I estimate it to be less than half of the times.
Boss Fragments
Try to have a waystone and tablets with as high waystone drop chance as possible. It gives a slight increase in chance to drop more than one fragment.
The Patriarch/Matriarch Halls
Guaranteed Fragment for Arbiter of Divinity
Very valuable throughout the league, especially at league start since people need it to finish their Atlas. Worth several divines each fragment usually.
The Iron/Copper/Stone Citadel
Guaranteed Fragment for Arbiter of Ash boss fight
Typically increases in value as league goes on as the boss do drop some items that are sought out after but usually rare.