Goku using the kaioken attack on vegeta
Kaio-ken Attack (界王拳アタック) is a rush attack used by Goku while using his Kaio-ken technique. Goku powers up to Kaio-ken x3 as he charges at the opponent and roundhouse kicks them up into the air. Then, he flies up in the air and punches the opponent away. Next, he flies up over the opponent and down behind to double kick them further up into the air. Finally, Goku flies up into the air around the opponent and hook kicks them down into the ground, inflicting a huge amount of damage.
Goku used this attack during his first battle against Vegeta. After being pummeled by Vegeta's increased speed and power even with his Kaio-ken x2, Goku decided to use his Kaio-ken x3. Goku charged up and his power soon surpassed that of Vegeta's, much to the Saiyan prince's shock and surprise. Activating his Kaio-ken x3, Goku charged at Vegeta and attacked him with the Kaio-ken Attack, knocking him meters away into a mountain. But, Vegeta recovered and continoued the battle.
Kaio-ken Attack was named in the Budokai Tenkaichi series and is one of Goku (Early)'s Blast 2 attacks. In Budokai Tenkaichi 1 and 2, the name was given to Goku's other Kaio-ken rush attack, Kaio-ken Finish. However, this was later fixed in Dragon Ball Z: Budokai Tenkaichi 3 and Dragon Ball: Raging Blast, whereas the latter features the Kaio-ken Attack and Kaio-ken Finish as seperate attacks.