I have no idea what the requirements for unlocking skills are. I unlocked Focused Aim and it has a number saying 4/6 - what does that mean?
This indicates that, among the 6 skills available to the Valkyrie class, this is number 4. The requirements to unlock the various skills differ; they depend on factors such as the number of successful hits, blocks performed, damage taken, critical hits or perfect blocks executed, and how many times you flee—to name just a few. These requirements are designed to accommodate each player's individual playstyle.
Well, it involves a lot of fighting.
You need to land 50 critical hits and 300 standard hits; have 120 of your attacks blocked by enemies; deal a total of 200 damage to enemies; successfully block 180 enemy attacks; kill at least 120 monsters; perform 25 perfect blocks; take a total of 500 damage in battle; land 45 preemptive strikes; dodge 25 times; successfully escape from combat 50 times; get poisoned by enemies 30 times; and receive 30 items during battle. By completing these tasks—which are largely random—you unlock all 6 abilities for each of the three classes.