Taking the same role as Kanade and Raki from the previous games, Akane can fight you up to three times, with her getting stronger between each battle. She is also accompanied by her loyal Antibody, Kukuro, and despite this battle being called an sparring match, it'll still cause you a Game Over if all your party members except your Reyvateil get killed, so be careful. You can start fighting her after seeing an scene at the Clustania Executive District, right after having defeated Richaryosha at the XP Shell and encountered Akane herself at Archia City. These battles are optional and thus, aren't required to beat the game, but you will gain some nice rewards if you win them. As a final note, you will have to leave the Executive District, return and fight five normal battles before Akane will be willing to challenge you again.
During this battle, Akane is even weaker than most of the bosses you have faced so far in Easy, but on the other difficulties, her stats are quite high and she can be quite problem if you aren't careful, so make sure to keep you HP high and try to avoid all of her attacks, since aside of hitting hard, she can also inflict your party members with all status ailments by simply attacking, like most bosses from Phase 3 onwards. Try to not pay much attention to Kukuro, but still, try to interrupt him whenever he tries using his Stored Attack, which would greatly reduce the speed at which your Burst Gauge increases. The same goes for Akane, as her Blade Gate skill can cause a tremendous amount of damage to a single character, most likely killing him/her. As long as you can withstand for long enough to use at least an Ultra Supermove, you should be able to win this battle, and get the ?Medical God Tool? recipe and an image for your Gallery as your rewards.
While in the other two difficulties Akane gets an average increase in stats, in Hard her stats receive a massive increase, making her a very dangerous opponent. In fact, at this point, she could easily kill your entire party in a single attack in both Normal and Hard if they are all unlucky to get caught in her consecutive slash move, so try to keep your distance from her and attack only whenever you see an opening. She also got a weakness to Paralysis this time around, so try to exploit it. As before, you shouldn't really pay much attention to Kukuro except to protect your Reyvateil, attain Beat Ups from him and cancel his Stored Attack. This time, you most likely will need at least two Ultra Supermoves and a Flipsphere to defeat her. Once you win, you will get another image for the Gallery and the ?Legend Board? recipe for your troubles.
This time, Akane got yet other average increase in both Easy and Normal, but in Hard, her HP is hitting the cap, her Attack is over 1300 and her Defense is around 980, making her not only extremely resilient, but also, perfectly capable of one-shooting any of your party members, so you will have to be even more cautious against her attacks. The same advice given for the second battle can also be applied here, but you will need to use all your Ultra Supermoves and at least one or two Flipspheres to take her down. Once you finally manage to defeat her, you will get the final image for the Gallery and the ?Mythic Weapon? recipe as proof of your victory.