It's not going to be like if you fight more monsters, you'll get more level ups, like similar to the experience system. Of course, if you fight against monsters, you will get some skill points, but it will help more if you attend to Guildleves. So that will be a more efficient way to hone your skills and 'level up' your character.
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FFXIV ZAM
Now, unless something was lost in translation, what I'm reading is that the primary way to level up is through these "quests". Maybe you are awarded skills for completing quests? Really interesting quote though...
