Where you farm Asterite depends entirely on which game mode you prefer or excel at, because both sources are equally viable if you have what it takes to get into the high rankings.
What is Asterite Used For?
Asterite is among the rarest and most valuable resources in the game. You can use them to buy items from the Asterite Exchange Shop. A lot of cosmetics and account growth materials are available here, but for F2P players, I recommend saving your Asterite exclusively for these items: You can also exchange Asterite for Territe, but this process requires Black Diamonds which are the game’s purely premium currency. As of this writing, there is no way you can earn Black Diamonds as a F2P player.
Where To Farm F2P Asterite
There are only two sources of F2P Asterite, and they both require you to play NNK:CW religiously and competitively. If you don’t have the qualifications to farm either of the two sources, then don’t worry — you don’t need Asterite to access or enjoy everything the game has to offer!
Source #1: Lava Valley
Lava Valley is Ni No Kuni: Cross World’s version of real-time PVP. Here, you can team up with two other players to participate in a 3v3 team battle. The more team battles you win, the higher your rank will be. Reach a high enough rank and you’ll be able to farm Asterite from weekly ranking rewards and season ranking rewards.
Source #2: Familiar Arena
If you’re consistently acquiring duplicate Familiars and feeding them enough Stretchy, Tough, and Fluffy Jellies to max them out, then the Familiar Arena is perfect for you. Unlike Lava Valley matches, Familiar Arena matches aren’t real-time. This means you can strategize and beat teams that are stronger than yours. You can farm Asterite by also climbing through the Familiar Arena rankings and acquiring weekly and season ranking rewards.