Hyper Mode is a special mode in the game Sonic the Fighters. It can be activated in any fight by all fighters in order to increase the speed of their moves and unlock access to special Hyper Moves. However, the fighters lose some of their shields in the process of doing so.
For the final fight against Eggman, the characters toss the Chaos Emeralds into the air right before fighting him. They activate it in order to beat Eggman in less than fifteen seconds and escape the destruction of the Death Egg II.