"Forge ahead" means (to increase your speed or take the lead) or ( to move forward steadily). The car forged ahead into first place. The boat forged ahead against the waves. "Up to the hilt" or "to the hilt" means figuratively (completely or to the limit) The players are in the game up to the hilt now. Literally, hilt is an old word that means the handle of a sword or dagger. He plunged his sword up to the hilt into the body of the dragon.