She looked like she had been ill for a long time.

Literal

She [topic-は] long time illness was [as if-ように] appeared.

~ように見えた ('looked like / appeared to be') combines ~ように (manner/resemblance) with 見える ('to be visible / to appear'). The speaker is making an inference from observation — she looked unwell, and the impression was of long-term illness. であった is the formal past of the copula, giving the embedded clause a slightly written quality.