To increase Corruption in Last Epoch's Empowered Monoliths, you must defeat the Shade of Orobyss, found in deeper echoes of the timeline web. You earn extra corruption by gaining and consuming Gaze of Orobyss stacks from defeating timeline bosses before fighting the Shade. Use Glyphs of Envy to quickly build stability and increase your chances for more Gaze stacks. 

If you are defeating Shades and your corruption is still not going up, check your Weaver Tree to see if you have the node "Purged Horizon" selected as it will prevent corruption gain.

To access your Weaver Tree:

1. In-game open your Faction window by pressing Y (default keybind).
2. Once in the Factions window, click on the Endgame Factions button.
   
3. Click on "Rank and Reputation" on The Woven.
   
4. Click on "Weaver Tree" within The Woven window.
   
5. Once on the Weaver Tree window, move towards the bottom left of the tree to find the node "Purged Horizon". If this is activate it will be colored in and not in black and white and say 1/1.