Usage patterns
〈事〉がうなぎ登りに上がるfor something to keep rising sharply
His popularity is skyrocketing.
〈物〉がうなぎ登りだfor something to be soaring/rising rapidly
Prices have been skyrocketing lately.
うなぎ登りに〈動詞〉to increase/rise steeply (used to modify a verb of increasing)
This shop's sales are rapidly climbing.