How to lvl Alva to lvl 7

To level up Zana, complete maps in your Atlas:
Complete 4 maps for level 2.
Complete 10 maps for level 3.
Complete 25 maps for level 4.
Complete 50 maps for level 5.
Complete 80 maps for level 6.
Complete 120 maps for level 7.
This does NOT require you to get the bonus objective for the maps.

To level up Alva, explore rooms in the Temple of Atzoatl.
Explore 15 rooms for level 2.
Explore 30 rooms for level 3.
Explore 40 rooms for level 4.
Explore 50 rooms for level 5.
Explore 60 rooms for level 6.
Explore 70 rooms for level 7.
"Exploring" a room is to simply walk into a room. Each room only counts once regardless of getting it again in another Temple. A T3 room counts as a T1 and and T2 as well, so a T3 room counts are exploring 3 rooms rather than 1.

To level up Nko, Delve deeper in the Azurite Mine:
Reach depth 10 for level 2.
Reach depth 20 for level 3.
Reach depth 50 for level 4.
Reach depth 90 for level 5.
Reach depth 140 for level 6.
Reach depth 200 for level 7.

To level up Einhar, capture monsters in the Bestiary.
Capture 5 monsters for level 2.
Capture 20 monsters for level 3.
Capture 45 monsters for level 4.
Capture 80 monsters for level 5.
Capture 120 monsters for level 6.
Capture 160 monsters for level 7.
Capture monsters you have already captured does NOT count towards this. You can view what you've already capture in the Bestiary in-game in the Challenge/Achievements Panel (default key "H") and navigate to the "Bestiary" tab.

EDIT:
For leveling Alva, Apex also counts as 1 room.