She does nothing but find fault with her neighbor.
Literal
She [topic-は] neighbor [possessive-の] fault-finding [nothing but-ばかり] is-doing.
あらさがし (粗探し, 'fault-finding') combines 粗 ('flaw, rough spot') with 探し ('searching'). ~ばかりしている means 'does nothing but X' — ばかり with ている emphasizes the habitual, persistent nature of the faultfinding.