Skilling high rarity cards poses an interesting predicament. That being that technically you can purchase HR for 1HP on a regular basis, either treasure HR or event HR. Also that you can purchase rares for 1CW each if you look around. But in both cases it is a pain to accumulate large numbers of rares or HR given the limitations of Bazaar tickets. Finally, by purchasing Skilled High Normals you get to purchase a rare for roughly the price of .4 HP per rare (which is what I consider roughly the cost of one CW) but you can attain them through feeder service. Either way, because of this my math on pricing will be done at the rate of 4HP per 9 Rares. If I use High Rares I will be doing them at the approximate price of 9HP per 9 High Rares.
*SIDENOTE* All my math is done assuming the use of 9 cards, in a vast majority of cases it is beneficial to use 10 cards, especially near the end. The reason for using 9 cards is because in feeder service you are normally only attaining 9 and most people skilling up will just use them instead of waiting for a 10th card.
*SIDENOTE* Thanks to Jean-Baptiste for linking chart and everybody who mentioned skilled cards increase chance of increase. Damn you all as well because it just gives me extra work.
Skilling an SSR (SR evolved into SSR)
Lvl 1-2: 9 Rares yielding 72% chance to skill up - 28% chance you will have to try again. Rough Price 4-8HP.
Lvl 2-3: 9 Rares yielding 48% chance to skill up - 52% chance you will have to try again. Rough Price 8-12HP
Lvl 3-4: 9 Rares yielding 36% chance to skill up - 64% chance you will have to try again. Rough Price 16-20HP
Lvl 4-5: 9 Rares yielding 28% chance to skill up - 72% chance you will have to try again. Rough Price 16-20HP
Lvl 5-6: 9 Rares yielding 24% chance to skill up - 76% chance you will have to try again. Rough Price 20-24HP
Lvl 6-7: 9 Rares yielding 20% chance to skill up - 80% chance you will have to try again. Rough Price 24-28HP
Lvl 7-8: 9 Rares yielding 18% chance to skill up - 82% chance you will have to try again. Rough Price 24-28HP.
Lvl 8-9: 9 Rares yielding 16% chance to skill up - 84% chance you will have to try again. Rough Price 28-32HP
Lvl 9-10: 9 Rares yielding 14% chance to skill up - 86% chance you will have to try again. Rough Price 28-32HP
Final rough price is around 190ish HP on average but can really increase heavily during the last three levels. During this time be sure to pepper in that 10th card. It still isn't worth it as far as I can tell to use HR at this point. The reason is that using it from 8-9 for example would be roughly 30% chance of success but would cost 10HP each attempt. You'll notice at that pricing it's starting to level out on price per percentage, but its close and a string of bad luck at 10HP per pop adds up fast.
Skilling a Legend (SSR evolved into Legend)
Lvl 1-2: 9 High Rares yielding 72% chance to skill up - 28% chance you will have to try again. Rough Price 9-18HP
Lvl 2-3: 9 High Rares yielding 48% chance to skill up - 52% chance you will have to try again. Rough Price 18-27HP
Lvl 3-4: 9 High Rares yielding 36% chance to skill up - 64% chance you will have to try again. Rough Price 36-45HP
Lvl 4-5: 9 High Rares yielding 28% chance to skill up - 72% chance you will have to try again. Rough Price 36-45HP
Lvl 5-6: 9 High Rares yielding 24% chance to skill up - 76% chance you will have to try again. Rough Price 45-54HP
Lvl 6-7: 9 High Rares yielding 20% chance to skill up - 80% chance you will have to try again. Rough Price 54-63HP
Lvl 7-8: 9 High Rares yielding 18% chance to skill up - 82% chance you will have to try again. Rough Price 54-63HP
Lvl 8-9: 9 High Rares yielding 16% chance to skill up - 84% chance you will have to try again. Rough Price 63-72HP
Lvl 9-10: 9 High Rares yielding 14% chance to skill up - 86% chance you will have to try again. Rough Price 63-72HP
Final rough price is about 420HP to max it. Before I went through this step by step I really didn't think I'd come to the conclusion that Devil Queens are way overpriced, but lo and behold. Devil Queens currently running for 130HP each which is absurd. That means that using a Devil Queen mimics the cost of my worse case scenarios using High Rares. Devil Queens should be 50HP each.
Unfortunately there is a time variable. Purchasing enough HR given the limited number of bazaar tickets would take some time. Devil Queens can be purchased much more easily and quickly.
*FINAL THOUGHTS* Overall I hate the topic of skill enhancement. I find it boring and too uncontrolled to be completely accurate with. Since it deals with percentages I can say that it will cost 72HP to level from 9-10 on a legend card but it could just as easily end up taking 50 attempts and then I get some angry person spouting on how I don't know what I'm talking about. I avoided this topic because it is based quite a bit around luck and only did this post because a few people asked for it. Do NOT expect future posts on skill enhancement unless something new and interesting occurs.