。
Ignoring the likes of me so casually — you've got some nerve.
Literal
This I [obj-を] casually ignore do-[that-とは] good nerve is-[わね].
ワタクシ in katakana for the haughty 'I' — an exaggerated, self-aggrandizing self-reference. さらりと is an adverbial mimetic meaning 'smoothly, lightly, without making a fuss.' The pattern ~とは here is a nominalizing とは (from と + は) tagging the preceding clause as a discussable proposition — 'the fact of ignoring me = good nerve.' 良い度胸 ('some nerve') is a fixed sarcastic formula used when someone has done something bold the speaker resents. ですわね is the feminine refined form — お嬢様 register.