This is the Kaio-Ken!! A Battle to the Limit of Goku vs. Vegeta

With Vegeta ready to enter the fight, Nappa realizes that he has lost, and decides to attack Gohan and Krillin instead. However, Goku disables Nappa by using his new Kaio-ken technique. With his partner now useless, Vegeta launches Nappa into the sky and mercilessly kills him with a powerful ki blast. Goku tells Gohan and Krillin to leave so he can fight Vegeta without distraction. After moving to a new battleground, the two remaining Saiyans begin their epic battle. However, Vegeta is much more powerful than Nappa was, and Goku eventually realizes that even the two-times Kaio-ken isn't enough to defeat his opponent. He then decides to break his promise to King Kai and risk his own life to use the three-times Kaio-ken.