。
She was practically jumping for joy.
Literal
She [topic-は] joy [too-much-のあまり] jump-up [as-if-about-to-んばかり] was.
Two patterns build the hyperbole. ~のあまり ('out of an excess of, so X that...') intensifies an emotion as the cause of the next action, attaching to a noun via の: 喜びのあまり ('out of overwhelming joy'), 悲しみのあまり ('overcome with grief'). Then ~んばかり ('as if about to, on the verge of') is a more literary register descendant of 飛び上がる + ~ぬ + ばかり: 'almost flying up.' The combination gives a doubly intensifying frame — joy so great that she was on the verge of leaping into the air, without quite doing so.