I remember that when you are cleaning out the tower with Simon in the party, you can actually meet mithyn for the first time in Tak'Kan Tower. But I decided to replay from scratch and forgotten how to meet her and even wiki doesn't show anything how to meet her. Help please.
Pretty sure the wiki does say in the section on the war but basically robin needs to not be injured and see her(gom) probe into the crossroads section
The https://thelastsovereign.miraheze.org/wiki/Erosian_War_guide page contains this info. In a nutshell: your "Robin Stand" score must be sufficient to avoid her getting injured, and she needs to interact with a sparkle in the Tower Crossroads (4) section. After that another sparkle in the Kanese Tower Foundation will trigger the conversation with Mithyn.
[EDIT] I've added a link/reference to this information on Mithyn's wiki page, so it may be easier to find.