How do you get past the Abykos in the Buried Crossroads without combat?

Solution 1:

Abykos feed on transdimensional energy. As far as I know, there is no way to avoid this fight apart from not looking into the central mirror.

Speculation here: Callistege is a transdimensional being, possibly, you could offer her as food. Though I doubt she likes that, even if it is possible.

Solution 2:

You can feed them The Foreman's Children.