Collecting the red death masks (hold B when prompted) and chaining attacks to defeat enemies will earn you XP.
During the first level you will reach 1000XP - this will allow you to press the BACK button and enter the upgrade menu. Simply choose to upgrade your standard blades and you will trigger this achievement.
While in the upgrade menu, press Y for combo training. Follow the button prompts (X and Y, with A for airborne attacks) and you will gain some extra XP for completing each move.