Probably you should use the verb 'superare'
"Outhustle" is a combination word that would be a colloquial version of "outdo", but implies working extra hard, moving fast.
"Hustle" means not only to move oneself or someone else quickly, but implies (in the world of business at least) moving into someone else's territory, fast-talking, or even flim-flammery. Think Donald Trump's reality TV show "The Apprentice". Implies getting ahead in business by both hard work and a bit of pressure.
"Outhustle" would be to compete with another person, for example, for a business account, or to win a prize, sell the most cars... with an incredible burst of energy, work, sweet-talking, whatever it would take to win.
So 'superare' is the closest I can think of, but doesn't necessarily carry all the implications.