This is a pretty straightforward (if time-consuming) achievement.
You need to maximize the friendship level with all ten of the non-DLC Masters. They are Goku, Piccolo, Krillin, Vegeta, Gohan & Videl, Captain Ginyu, Frieza (1st Form), Android 18, Cell (Perfect), Hercule, Gotenks, and God of Destruction Beerus. (None of the DLC Masters count for this achievement, just like their Super/Ultimate moves don't count for the Skill collection achievements).
The fastest way to build up friendship is to just do the fastest Parallel Quest that you can. Each time you complete a PQ, their gauge will go up a tiny amount (the first and last 3-5 seem to be covered by the gauge's edge, so they will seem to have no gain even though they really do).
However, I recommend focusing on collecting all the Super/Ultimate Skills from each of the non-DLC PQ's first, since if you care about achievements then you'll be wanting those anyway. Two goals at the same time, saves at least a bit of time in the long run.
There is a set of advice that most people share: Have your Master on your team (as well as your custom character), have their moves in your current skillset, and equip the masters' Z-Soul.
However, from my own testing, I don't really think that any of those actually make the gauge go up any faster. But if you want to do so, go ahead, no reason not to! (And if you track it and find there is a real difference, please post it! It's always seemed like an assumption from others, since I never found anything that suggested it was actually tested by anyone.)
Either way, you only need one instance of your Master in your team (many people say you should have two, but I didn't notice any increase or loss by having either one or two).
In the case of Gohan & Videl, it seems Gohan may be the one that matters for this, though that is not really verified.
When you complete your training with one Master, you then want to minimize the amount of time spent hunting for the next one. A couple of things:
1) Only one Master at a time will appear inside the whole city for you to start (or resume) training. There are 3-4 locations in each of the three regions of the city that they might appear, and it is a random person in a random location each time the city is reloaded. This means it can take a LOT of reloads before the one you want appears.
2) Whenever you enter the Character Select screen for either Parallel Quests or Battles (either online or offline), the town reloads so you can most quickly reroll which Master is in the city by just entering the character select screen as fast as possible and then backing out immediately to the city to search for the Master that has appeared.