Well, her first scene has her and alyssa in a dressing room trying out dresses, and the MC is also there, hiding in one of the stalls. Eligos tries to direct Alyssa to that stall (so she can do it with the MC) but she says there's no reason to because they're both girls, so Eligos goes there instead. Thus, the MC does it with Eligos, and she notes how the MC does have feelings for Alyssa, and asks him to imagine the three of them together. During this whole time, Alyssa is still on the other side of the curtain trying on dresses and talking with Eligos (note how Alyssa is in the background... again).
As for the second scene, Eligos approaches the MC late at night in a castle (presumably one they helped in her intro scene), and tells him she has a power of prophesy (in addition to her power of love), and that she saw a future in which she had the MC's child (go figure). Apparently the previous times weren't enough, so she asks you to do it one more time, which the MC obviously complies with. Not much more to that scene.
If you have any more questions related to Eligos, feel free to ask!