How to unlock champions
The first twelve need no unlock. Event champions return in time gates. Five evergreens below have a named variant or a newsletter.
Unlocks with a citation
The official FAQ splits the roster into the starter twelve, event champions (events, time gates, or the shop), and evergreens tied to variants. Windfall clears Double or Nothing on The Rod of Seven Parts. Wren clears Twice Through the Great Wheel on Titan on the Town. Blooshi clears Bully For You! in Witchlight. Azaka clears Azaka's Procession - Part 2 in Tomb of Annihilation. Hitch is the newsletter signup, not a variant.
I am not extending that list to every evergreen. If a name is missing, the champion table still shows the unlock field when the wiki table had one, and the cell stays blank when it did not. Other evergreens stay in that table until their variant text is in front of me.
FAQ
How do I get Hitch?
The official FAQ says the newsletter signup unlocks Hitch.
How do I get Azaka?
Clear Azaka's Procession - Part 2 in Tomb of Annihilation.