These achievements are not that hard to complete. However, most people don't really understand what it means. So, here's how it works:
Each officer can acquire 1 ability per battle and earn a total of 4 abilities (sometimes 3). To earn these abilities certain requirements must be met. Some are easy (Like "Kill 50 Enemies" & "Defeat 3 Officers) and become harder over time ("Kill 100 enemies, never go below 50% health, and don't use Musou").
To check the requirement go to the "Team Info" menu and, if they can earn an ability, there will be a menu called "Ability". Go into it and it will tell you what you need to do.
To check your total level of abilities go into the ability menu and off to the right of the name of the ability there will be a number. Add all the numbers up and that is your total.
For this achievement, you require a total of 30.