Here is the full list of all 46 Monster Girl Manager achievements.
Activate an orb overflow
Have 10 or more frenzy in battle
Have armor higher than maximum health
Summon a girl from a special seed.
Use Hammer Smash with a berzerk axe and quick knife equipped.
Give mile stone dust to a monster girl
Train a monster girl to max level
Have map vision of 5 or more
Use Stab with the plague mask, poisoned blade, and venom moss equipped
Use Hellfire with the fuel tank, hot brand, and magnifying glass equipped
Have 5 monster girls in town at once
Have a moth swap while carrying a mood ring
Use home run on a trapped enemy with a lamia
Use shield bash with over 99 armor on a cyclops
Use sniper on an elf while carrying a spyglass and an ice pick
Equip trail mix, sleeping bag, smores, and old compass simultaneously
Use dark ritual while carrying a black donut
Use GET DOWN! with a proximity mine and dead mans switch
Use tsunami with a wave pendant and shallow bowl
Enter a boss fight with a broken chain, giant killer, and glass parasite equipped on one girl.
Skip a turn with a green mushroom and playing cards equipped
Use first aid with a med kit and a clean slate equipped
Use a skill on an ally with the blessed egg and tinfoil hat equipped
Equip a lava rock, fireworks, and candle wax
Equip a healing sword, a beating heart, and a holy scripture
Use venom fang with venom moss and venom gland equipped
Defeat a dungeon's final boss with only 1 monster girl left
Equip broken glass, mutant serum, and bottled lightning
Equip a dwarf moon, a harvest moon, a blood moon, and a hidden moon
Equip 2 of hearts, 10 of clubs, and house card
Equip an arachne with a tangle bomb and a mousetrap
Use horse code on a kitsune
Equip a kitsune with a geode
Equip a lamia with a ghost anchor
Use pollinate on an Alraune
Equip a nickel sock and golden armor onto a Dragon
Use Infect with a plague essence and a plague mask equipped
Equip a blood goblet and vampire fang on a vampire
Use moon light on a werewolf
Use fists of fury with an orc while carrying a boar pendant
Equip a geode and a colored stone to a golem
Equip a Glass Eye and an Evil Eye onto a Cyclops
Have an angel sound the Angel Trumpet
Equip a beating heart onto a Robot.
Use the restful melody skill with the War Drums
Equip a Mist Totem and a Smoke Cloak onto a ghost