To unlock Veni, Vidi, Vici, you must complete the game on any difficulty. Basically, complete the game for the first time.
There are eight chapters within the game, averaging at about 30minutes in length.
I would suggest doing your first playthrough on either soldier or beginner difficulty, as you have to play it again on legendary, so might as well level up before hand. Jumping right into Centurion with no upgrades might prove tricky for some.