Legion Training

Roman Fighting is the fighting style that the Roman Demigods use in Camp Jupiter. The general that normalized training and equipment was Marcius, close before the time of Caesar. Heroes of Olympus

The Lost Hero
As shown by Jason, it's mostly about learning your opponents fighting style and then adapting to it. This style of fighting is most effective when in groups. When Jason was fighting Lityerses, he started analyzing patterns and learning his style, (no defense, only offense) then countered, sidestepped, and blocked which Jason said was legion training, most likely because he fought in a way to oppose Lityerses.

The Son of Neptune
During the war games, Percy's unorthodox, solo, unpredictable fighting style was dangerous for the campers at Camp Jupiter because they are used to fighting in a group in an organized way. Because of that, Percy was able to take down multiple enemies at once, causing mass panic.

Later on in the book, while escaping the Amazons, when Percy sidestepped, hacked a spear in half, and the hit the warrior with the butt of his sword, Frank pointed out that it wasn't any Roman technique.