さまざまな才能に恵まれて、なんでもそつなくこなす姉にとって、平々凡々たる俺の存在はひどく許せないものらしい。

、、。

For my sister — who's blessed with all kinds of talent and handles everything flawlessly — my utterly mediocre existence is apparently something she can't stand at all.

Literal

Various talent [to-に] blessed-[and-て], anything flawlessly handle sister [for-にとって], utterly-mediocre [attr-たる] I [gen-の] existence [topic-は] terribly cannot-forgive [nominalizer-もの] seems.

A long, self-deprecating sentence describing a sibling dynamic. 恵まれる ('to be blessed') is a passive-form verb that takes に for the thing one is blessed with. そつなくこなす is the collocation for 'to handle flawlessly' — そつ meaning 'flaw/slip,' and こなす 'to handle / get through.' 平々凡々たる uses the classical attributive たる (equivalent to modern な), marking the adjective as elevated/literary. ~にとって frames the perspective: 'from [my sister's] point of view.' Final らしい is hearsay-ish: 'apparently / seems to be.' The whole piece captures that familial self-deprecating narrator voice.