Moe Chronicle

As you explore the different areas, you will come across monster girls who move around the map each time you do (like the FOEs in the Etrian Odyssey series). Fill up Otton's heart gauge, either by repeatedly attacking the girl with her weak element without defeating her, or by destroying all the parts of her costume. Then you'll play a mini-game called a "Bumping Scratch" where you try to fill up a gauge by touching the girl in the right places and in the right way, using the Vita's touchscreen. Succeed at this and you can use her as a party member. Do this for every monster girl in the game and you'll unlock this trophy. You will need to play through the post-game sealed areas to find some of them. There are a total of 50 monster girls in the entire game. You can check how many you still need using the "Pictorial Book" option at the inn.

A list of the monster girls and their general locations:

Mushroom Forest (1st Region): Lilia, Leche, Orthros, Goblin, Slime, Latte, Killer Bee, Orc, Fungus, Kobold

Sticky Greasy Lake (2nd Region): Calypso, Imp, Banshee, Will-o'-the-Wisp, Elf, Siren, Kentauros

Nude Lady Ruin (3rd Region): Typica, Mummy, Jack-o'-Lantern, Dark Elf, Ogre, Wight 

Inner Beauty Garden (4th Region): Ellie, Minotaur, Kamaitachi, Azuki Arai, Dragon, Orihime

Gothgal Quartz Area (5th Region): Mocha, Mattari, Necromancer, Talos, Dullahan, Chimera, Mimic, Istasia

White Limit (6th Region): Ranju, Jack-o'-Frost, Scylla, Gargoyle, Cerberus

Post-Game Sealed Areas: Griffin, Ziz, Behemoth, Valkyrie, Vampire, Leviathan, Satan, Coco
Most of the monster girls are not too difficult, especially if you're playing on Easy. If one is too tough, you can always come back after you've leveled up. They disappear briefly after a failed capture attempt, but will return. There are few that you might have trouble with:

Gargoyle:

The Bumping Scratch mini-game with Gargoyle may give you some problems. The area on her left ear (on your right) seems to be very small and doesn't always seem to respond properly. I've found it's best to just tap it quickly and repeatedly, which gives you stars rather than hearts - an indication that you're touching the right spot, just not in the best way, so the gauge still fills, but slower. Once you stop getting stars, quickly switch to her left forearm (on your right) just below the armband and tap there. Then move to her right breast (on your left). If you tap quickly enough, you should fill up the gauge in time.

Mimic, Scylla, Jack o'Frost and Ranju:

These four girls tend to pretty consistently dodge or block any attacks on their costumes, unless you hit the girls themselves enough to temporarily knock them out. Then you can focus on the individual costume parts. Once you get them down to their final health bar, your costume attacks won't miss nearly as much.

Vampire:

Vampire attacks with four strong monsters and together they can hit pretty hard. If they're knocking you out before you get a turn, equip accessories that increase agility. Make sure the characters with DEF/MDF up skills use them before attacking, and use "Party Heal" regularly. Take out the lesser monsters first using Aura-Attack combos or the Sadist moe trait combined with Otton's fury. Getting the Ultimate Pantie first will also help. (It's at X:11 Y:10 on the Gothgal Quartz Area 7F Sealed Floor.)

Ziz:

Ziz isn't difficult at first, but once you destroy one of her costume pieces she'll hit you with a massive double attack that will most likely wipe out your entire party no matter what level they're at. To avoid this, get each costume piece down to about 10% health, but do not destroy them. At this point you may want to deliberately avoid aura combos, as Otton's fury attack can sometimes inadvertently destroy a costume piece and trigger Ziz's power attack. Once you have all three weakened, wait until she attacks to give yourself as many moves as possible, then release Io and use your strongest skills. You should be able to take out all three pieces before her attack turn comes around again.

Satan:

She is by far the hardest fight in the game, even more so than the final boss. Before battling her, obtain the Ultimate Pantie (it's at X:11 Y:10 on the Gothgal Quartz Area 7F Sealed Floor) and equip it on your heaviest hitter. It gives a massive stat boost but there is only one in the entire game. Also, equip accessories that prevent paralysis (not just reduce the chance) on as many characters as you can, starting with your healer and anyone with the "Recover" skill.

She starts out alongside two Wrathful Tadpoles and two Gaudy Condogolems, which can easily decimate your party. Concentrate on those first, using the aura attacks that they're weak to, along with skills to boost your DEF and MDF so you'll have a better chance at surviving 2 or 3 big hits in a row, which happens frequently. Once you get Otton's fury up to the maximum level, keep it there by not letting the aura combo get any higher. This increases the attack of your entire party +50% for each Sadist in your party.

If you have a character with the "Call of Death" insta-kill skill (Scylla for example), use that on the lesser enemies. The insta-kill is based on chance, so you can't rely on it entirely, but when it works it's the fastest way to get rid of them, and it always does decent physical damage regardless. Use "Party Heal" copiously, and remember that Io can use items as well. This can be a frustrating battle because there is no convenient save point, so defeat means trudging back through the lower floors of the dungeon again. Use your best healing and resurrection items; this is what you've been saving them for. If all else fails, level up some more and try again. The lowest level party I've been able to beat her with was around level 70 on Easy, and that was with several resurrects. Higher level characters are always better.

Once you get rid of the four lesser enemies, the fight becomes much more manageable. But she does have one attack that paralyzes your entire party (thus making you instantly lose the battle), and she will hit you with it once you defeat the other enemies. This is why it's vital that you have anti-paralysis equipment on as many characters as possible. The good news is that Satan's Bumping Scratch is pretty easy, so you shouldn't have to worry about failing it and having to fight her again. If you're concerned about that, attack her body and not her costume so you get the "Gentleman Bonus" which gives you additional Bumping Scratch time.