Her manner is free of affectation and artificiality.
Literal
Her attitude [topic-は] pretension [and-や] artificiality [subject-が] not-exist.
気取り 'affectation, putting on airs.' わざとらしさ 'artificiality, being obviously fake' — the noun form of わざとらしい. がない 'lacks, is free of.' A compliment about natural, unpretentious behavior.