を頼りに => to rely on / with the aid of something N2
~みこみだ => ~Expected N1
Determined, determined
~みこみちがい / みこみはずれ> => ~Contrary to expectations N1
Beyond expectations
み => ~ness N3
を[頼「たよ」]りに => With the help of A; thanks to A N2
Based, Focused, Depending on
~みこみがたつ => have a good prospect N1
Expected
とみえて/とみえる => It seems that ~ N1
... はずみ.... => So N2
Result
~みこみがある => There is hope, there is prospect. N1
にみる => Seen before N3
Base, base
てみる => Try somethjng N4
... みます => try doing ~ N4
Conjugate verbs