In order to complete training with Krillin, you must first accept him as your master. You do this by finding him standing in one of the areas of the TokiToki Tower. I found him in the Plaza of Time, however I believe the NPC's move around as time goes on. You can identify a master because they have a unique symbol next to their name. After you accept a master, you'll find them standing in front of the space ships in the South East corner of the Time Machine Station.
As with any master, Krillin will first wish to test your skills. After a brief fight, he'll concede and agree to be your master. He'll then teach you "Orin Combo", which is a strike skill. You must then press
and go to "Change Skill Set". Equip the move and then make sure to use the move in battle as much as possible. Also, have Krillin fight alongside you when you're completing Parallel Quests and things of this nature. Both of these boost favor.
After a few fights, search for him at the Time Machine Station. Once you can advance your training he will have a special interaction with you and you'll face off again. The second time, he'll give you his technique "Destructo Disk", A "Ki Blast" special attack. Repeat the process above. The third and final skill he gives you is the "Spread Shot Retreat" which is an evasive skill. I used this paired with Destructo Disk to gain favor while having him fight by my side. Continue to do this and you should earn the final battle with him, which will net you this achievement and the "Scatter Kamehameha" Ultimate Attack. It's worth noting his last battle must be a win with Destructo Disk. The one prior must be won with the Orin Strike.
You can only have one master at a time, so make sure you're ready to spend some time with whatever master you currently have. After finishing your training with Krillin, you'll keep your progress and be able to find a new master. You can also stop mid-way if you feel like it and resume later.