Complaining she was dead tired, she threw herself onto the couch.

Literal

She [topic-は] tired die-seems [quotative-と] complaint saying [while-ながら] couch [to-に] self [object-を] threw.

死にそうだ ('about to die') is hyperbolic — common in casual complaints. 身を投げる ('to throw oneself') is dramatic. ~ながら links the complaining to the action.