。
She's doing her best to act as kindly as possible.
Literal
She [topic-は] [as much as possible-できるだけ] kindly [is-behaving-ふるまっている].
できるだけ is the everyday-register counterpart of できる限り — both mean 'as much as possible,' but できるだけ is what you'd hear in conversation. ふるまう ('behave, conduct oneself') is the standard verb for outwardly visible conduct, distinct from 行動する ('act, take action'). Pairs with adverbs of manner: 親切にふるまう ('act kindly'), 大胆にふるまう ('act boldly'), 子供のようにふるまう ('act like a child'). The ~ている here marks ongoing effort — 'is in the process of behaving kindly.'