Little known fact that Iruli, one of the npcs on the LCS Daybreaker, has a titles and achieves for learning the skills that she sells. There is a trick to it so make sure to follow the steps exactly.
As you battle on the LCS, you will get courage points for each mob and boss killed. The amount that you get depends partly on the points that the mobs reward, partly on how fast you kill the boss, and partly on how many deaths you have had (more deaths = less points, and all deaths in the party count). You can keep track of the courage that you earned via a meter that pops up on your screen when the instance starts.
Iruli is one of the three npcs on the ship. She has the shop for the skills.
She sells two sets of skills: Melodies and Grimoires. Melodies is the hardest achievement here to complete, so we'll start with the Grimoires.
The Grimoires take less courage to complete at a time, so these are good to do when you don't have the 4793 courage necessary to complete the Melodies.
You don't have to learn all the Grimoire sets in one instance, which also makes these easier than the Melodies. You can learn a row at a time and work on them each time you get an LCS.
You want to make sure that you have 3 spaces open in your bag. Buy the three skills of the grimoire that you want to learn. Make sure that they are in your bag in order! You must learn each of the skills in a set in the order they are (left to right) in the shop menu.
If the last boss is killed, it is very important that you get each of the three in your bag FIRST, make sure they are in order, and then click them to learn them IN ORDER as fast as you can click. Once the last boss is killed, the buff from each level only lasts less than a second, so if you don't learn the next one before the buff from the previous one is gone, you can't learn the next skill - it will tell you that you don't meet the requirements. You can avoid this by learning them while you are still battling things since the buff will remain until the boss is dead.
However, if you have not learned your melodies yet, and it's looking like you might reach the necessary 4793 courage to learn the melodies, you may want to wait to see.
The melodies consist of three sets: Attack, Defense, and Life. To get the achieve, you must learn all three sets in one instance run. Each of the sets costs a little different, but in total, you need 4793 courage to buy them all. (*9/14/18 uodate: Powdy says that you actually only need to buy the very last of each set and use them to get this achieve, so give it a try! -- I did try this and it does let you use the last one. The total points needed for those is 974 for attack, 584 for defense, and 389 for life - 1947 )
I highly recommend that you learn them a whole set at a time so that you don't lose track of what you've already learned and what you still need to learn. Just like the grimoires, if you learn them while the battle is still on, the previous buff remains - AND if you wait until the final boss is killed, you have less than a second to learn the next level of each set.
For both the grimoires and melodies, it doesn't matter which set you
learn first, you just need to learn the skills in each set in order.
You can check your achievement progress here :
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