This chapter of the guide to Dragon Ball Z: Kakarot has a walkthrough for Between Worlds side quest.
Time frame: From Android Terror Arrives - Episode 8: Fleeting Normality to Episode 9: Gohan Unleashed
Reward: 136,715 EXP, 2x D Medal, Super Awesome Book for Grown-Ups
Where to start: Far Southern Islands Area, as Goku.
To start this mission, you need to go to Papaya Town and talk to Baba. Your task is to go to three places marked on the map and defeat opponents.
You must fight three enemy groups. They may have a slightly higher level than yours, but this shouldn't cause you problems.
Defeat all the enemies and then go back to Baba to receive the rewards.