。
She raised her children to be honest.
Literal
She [topic-は] children [object-を] honest is [as-ように] raised.
正直であるように育てる ('raise [someone] to be honest') uses ~ように with a stative predicate ('to be X') for the goal of upbringing. The である form is the literary/formal version of だ — common with na-adjectives in formal writing. 育てる ('to raise, to bring up') is the transitive verb of upbringing; intransitive 育つ ('to grow up') describes the child's perspective. The pattern [property]ように育てる is a standard way to express raising someone with a goal in mind.