Perfect Blue

The "Perfect Blue" title comes from the achievement "Something Borrowed," which requires you to beat level 25 in the Masked Carnival ("Dirty Rotten Azulmagia") while getting the following bonuses:

Can't Touch This

To get this bonus, you must take 0 damage throughout the entirety (i.e., all 3 acts) of the fight; this includes damage dealt to you by the boss's reflective shields, of which he has 2 types depending on which act you're in:

Ice Spikes. This reflects all physical attacks. Casting magic attacks or unaspected attacks will not hurt you, but casting physical attacks (including Fire Angon, which is a "physical fire" spell) will. I've seen people in various comment sections complaining about the boss's auto-attacks, which he does not have - if you're getting hit when the boss is not casting something, it's because you're stepping in an AOE or taking damage from his shield. If you are close enough to him to do a melee attack (e.g., when you step in to avoid The Dragon's Voice or use Sharpened Knife / J Kick), your character may be auto-attacking him, and so if he has Ice Spikes up, you will hurt yourself; however, it is you attacking him, not him attacking you, so make sure to either have auto-attack turned off or keep your distance. If you're having the auto-attack issue when getting in close to use some of your spells and for some reason don't want to turn auto-attack off, just save those that require you to be in close (e.g., Sharpened Knife and J Kick) for the Blazing Angons in Act 2. There is no timer on Ice Spikes and it will stay up until the end of the current act or until Azulmagia casts Repelling Spray to replace it.

Repelling Spray. This reflects all magical attacks. When the boss has this shield up, you cannot cast any non-physical spells on him or else it will reflect and do damage to you. This (unintuitively) includes things such as unaspected damage spells (e.g., Devour and Song of Torment) and debuff spells (e.g., Off-guard). If, however, you use Off-guard and Song of Torment on the boss before he casts this shield, the ticks from Song of Torment will not hurt you.

It is important to note that using Final Sting or Self Destruct do not count as taking damage, so (as of the date of this post, at least) you can Whistle + Moon Flute + Final Sting the boss as he's casting Meteor in Act 3 and still get this achievement. With the addition of the "Brush of Death" effect, you can no longer use it more than once during these runs due to the "Too Fast, Too Furious" bonus requirement (below).

Several of you have commented that using Devour will cause you to not get this achievement, but this is not true - I just tested this myself. If you don't believe me, go into an easier level in the Masked Carnival (e.g., level 5 with the three turtles that will not attack you) and try it out. Devour will, however, cause you not to get the next bonus.

Ain't Got Time to Bleed

To get this bonus, you must heal 0 damage. As pointed out by u/reiswindy below (thanks for catching this!), this bonus is what will cause you not to get "Perfect Blue" if you use Devour in this fight (as Devour heals you for the damage you deal with it). I just tested this myself and this is indeed true. It is worth noting that the only slightly difficult thing about all 3 acts of this fight is avoiding the boss's version of Plaincracker in Act 1, where the boss will put out a circle AOE around him, followed by 2 donut AOEs that will detonate, followed by 2 more donut AOEs that will detonate, followed by a cast of a really wide frontal conal attack called Apocalyptic Roar. I just tested this out as well, but you can avoid only the circle/donut AOEs and stand in the conal attack and continue to burn him down. The conal attack will put a doom debuff on you, but you cannot remove this because casting Exuviation also heals you and so you will not get the Ain't Got Time to Bleed bonus. Fortunately, you should have plenty enough time to finish the boss off before your doom timer is up, and you can still get both the Can't Touch This and Ain't Got Time to Bleed bonuses because doom is technically not "damage." The same goes for Act 3 when the boss casts Apocalyptic Roar again - you should be able to burn him down low enough to use Whistle + Moon Flute + Final Sting before the doom timer (and Meteor cast) expires, so there's no need to waste time side stepping this attack.

In light of the foregoing, I have not tested this yet, but I'm fairly certain that you can use Devour on Siegfried in level 30 and still get the Champion of the Blue title because you do not have to get the Ain't Got Time to Bleed bonus in that fight; you must cast Exuviation to get out of Ankle Graze, and thus you heal yourself in that fight, so I'm fairly certain that this bonus is specific to the Perfect Blue title.

Total Mastery

To get this bonus, you must use 1 spell of each of the elemental (water, wind, earth, lightning, fire and ice) and physical (blunt, piercing and slashing) types. You just have to use each spell at some point during any of the 3 phases - if you use all of the types during the 1st phase but not the 2nd and 3rd phase, for example, that is sufficient. The key here is to *use* the ability - you don't actually have to hit the boss with it (although that's better because it makes the fight go more quickly). For example, casting Ice Spike would count as using an ice ability even though you're not allowed to get hit, as would using an ability that misses the boss. Obviously use whatever is easiest for you, but here is a list of the options as of the date of this post - I've listed those first that I used when I ran this, but have included other options for each category as well in case you don't have the recommended spells:

Water: Protean Wave (#51) | Water Cannon (#1) | Aqua Breath (#3) | Hydro Pull (#97) | Malediction of Water (#98)

Wind: Sonic Boom (#63) | Feather Rain (#44) | Alpine Draft (#50)

Earth: Surpanakha (#78) | Plaincracker (#11) | Mountain Buster (#46) | Feculent Flood (#87)

Lightning: Shock Strike (#47) | High Voltage (#6) | Glower (#10) | The Dragon's Voice (#34) | Electrogenesis (#53) | Reflux (#74) | Tingle (#82)

Fire: Eruption (#45) | Flame Thrower (#2) | Bomb Toss (#19) | Mustard Bomb (#94)

Ice: Glass Dance (#48) | The Ram's Voice (#33) | Northerlies (#52) | Blaze (#93)

Physical - Slashing: Sharpened Knife (#15) | Kaltstrahl (#54)

Physical - Piercing: Abyssal Transfixion (#55) | Drill Cannon (#5) | Flying Sardine (#24) | 1000 Needles (#36)

Physical - Blunt: J Kick (#80) | Flying Frenzy (#4) | 4-tonze Weight (#26) | Mountain Buster (#46) | Peripheral Synthesis (#101)

Too Fast, Too Furious

To get this bonus, you have to clear the fight within the ideal time, which for level 25 is 7 minutes and 15 seconds. This should be plenty enough if you have all of the spells. (When I do this run it usually takes me around 4 minutes or less). It is worth noting that the timer never stops ticking - it's counting down from the second you enter the fight until the moment you kill the boss in Act 3, and this includes the time between acts when the screen goes black. Again, though, this shouldn't be an issue whatsoever.

Just a random tip about this fight, but from my experience the blazing angons that he throws down are strong against magical and unaspected damage (they do almost no damage whatsoever), so you'll need to use physical attacks to quickly eliminate them before they can cast Burn.