How do you get kaioken & kaioken 3x on the mission invade earth

Hello Dalton.

I'm sorry I'm a little slow getting an answer to you about this mission. I'm only just getting active on the site again, so I hope you'll excuse the lateness.

First off, let me say that this game's rewards and triggers are controlled by a highly impartial Random Number Generator (RNG) for it's decisions. With that in mind, understand that you will be given the pleasure of repeating quests over and over if the RNG doesn't pull the right number for you.

Onto the mission you're asking about:

Invade Earth, like all missions I've seen thus far, have three different versions of it's win conditions. The primary win condition is to simply defeat Goku. That much alone will constitute a the XP growth and your Zeni.

If you manage to complete the battle against Goku with Nappa still alive, you will pick up the first advanced win condition. This gives a possible trigger to pick up extra quest rewards.

Specifically for Kioken and the x3 variant, you will need to beat the mission with Nappa not only alive, but with more than (I believe) 50% health. If you manage to do that, Goku will stand back up and use one of the two Kaioken techniques. If the RNG is in your favor, you will get the ability. If not, you will complete the fight, and have to repeat it.

Sadly, while the game is good, the RNG does detract from it some. I know it took me about 40-45 tries before unlocking "I'm the strongest on Earth" Z-Soul in PQ5: Attack of the Saiyans

Keep your head up, pay attention to Nappa's health, and eventually you'll get them.

Hope that helps.