For each map completed under certain conditions, you gain an Atlas completion Bonus.
Defeating the boss is often the bonus objective for the Atlas of Worlds completion, with higher tiers requiring the map to be crafted in a certain way.
Map drops bonus
Each Bonus adds a 1% chance for a map to drop one tier higher, with each 100% chance automatically upgrading the tier of the dropped map. The maximum map tier, however, cannot bypass drop restrictions, even if it would have been upgraded.
For example, a rare monster in a tier 6 map with 125% completion bonus:
a rare monster can drop tier +1 maps, as such it can drop tier 1 to 7 maps
it will only drop maps that are adjacent or already unlocked (completed) on the atlas
a tier 5 drop would be upgraded to tier 6, with a 25% chance to be upgraded to tier 7
a tier 6 drop would be upgraded to tier 7, but can’t be upgraded any further
a tier 7 drop is already the highest possible drop, and can’t be upgraded any further