In-Game Nick: SummerSnow, Level 65 Woody Priest in Guildless Wonderland

Objective
Below is an unverified translated list of monsters that drop materials that can be used to craft equipment with special status.

Boost Dodge Rate [Armour]
Note: Reduce monster hit accuracy.

Lizard (Level 6, 11, 13, 16, 18)       
Ice Toad (Level 46, 58)
Turtle (Level 83 at Soul)

Boost Strike Rate [Weapon]
Note: Increase the player hitting accuracy hence reduce missed hit.

Bear (Level 21, 23, 26, 31, 33, 36)
Man-faced (Level 41, 43, 46, 48, 56, 58)

Boost Attack Speed [Weapon]
Note: Increase the attack speed of the player.

Leopard (Level 21, 23, 31, 33, 36)
Ghost Soldier (Level 21, 23)
(Level 81 at Soul)

       
Increase damage when HP is low [Jewellery]
Note: When the player's HP is less than half, there's a chance of delivering 1x-4x of damage.
The lower the HP, the greater the damage.

 
Rabbit (Level 1)
Ghost Soldier (Level 18)
Hell Hound (Level 61, 66, 68, 76) 

Restore HP after killing a monster. [Leather]
Note: Restore some HP after killing a monster, no effect on PKing a player. 

Newt (Level 21, 36, 38)
Man-eating Flower (Level 46, 53)
(Level 81 monster at Soul, not sure its name)

      
Restore MP after killing a monster. [Weapon]
Note: Restore some MP after killing a monster, no effect on PKing a player.

Fox Goblin (Level 41, 43, 46, 48, 56, 58)
(Another level 81 monster at Soul, not sure its name)

Dispel Evil [Leather]
Note: Each attack has a chance of removing the monster's aura.

Macaque (Level 8, 11, 13, 16, 18)
Ghost Soldier (Level 18)
Bat Goblin (Level 43, 53)

       
Decrease opponent's MP [Armour]
Note: Each attack has a chance of decreasing the monster's MP.

Eagle (Level 36, 38)
Bat Goblin (Level 53)
Corpse of Bladed Soul (Level 61, 63, 66)  

Decrease damage received [Armour]
Note: Decrease some damage from each attack received.

Wild Boar (Level 11, 13, 16, 18)
Two-Head Monster (Level 61, 63, 68) 

       
       
Increase HP Max [Jewellery]
Note: Increase player's maximum HP.

Wood Monster (Level 41, 43, 48, 56, 58)

Increase MP Max [Jewellery]
Note: Increase player's maximum MP.

Lizard (Level 6, 11, 13, 16, 18)
Crocodile (Level 21, 26, 28, 33, 36, 38)
GreenTail (Level 61, 63, 68, 71)

  
Double Attack Rate [Jewellery] 
Note: A chance of inflicting double damage with each attack.
Note: A must for paladin.

Tiger (Level 21, 26, 28, 31, 33, 36)

Absorb HP [Armour]
Note: Every hit on the monster (no missed) will increase some player's HP.

Wild Bull (Level 8, 11, 13, 16, 18)
Newt (Level 21, 36, 38)
Wood Ghost (Level 61, 63, 66)

       
Absorb MP [Jewellery]
Note: Every hit on the monster (no missed) will increase some player's MP.

Fox (Level 21, 23, 28, 31, 36, 38)
Snake (Level 63, 66, 68, 78)

       
Increase Attack Power [Weapon]
Note: Self-explained.

Big Mouth Rampage (Level 61, 63, 66, 68, 78)

       
Blindness to defense [Weapon]
Note: A chance to ignore the opponent's defense with the strike.

Spider (Level 3, 6)
Wood Spirit (Level 61, 66, 68, 73, 76)

Increase defense [Jewellery]
Note: Self-explained.

Deer (Level 6)
Man-faced (Level 41, 43, 46, 48, 46, 58)

Damage Rebound [Armour]
Note: A chance to rebound the damage to the enemy.

Giant Mosquito (Level 26, 28, 36, 38)
Golden Ape (Level 53)
 (Level 88 monster at Soul, not sure its name)

Charge Resist [Leather]
Note: Reduce the chance of being attacked by special status. (Eg. critical hit, double attack, hit to floor)

Tiger-Faced Man (Level 21, 28, 33, 36)
Two-Head Monster (Level 61, 63, 68)

Back-stabbed Attack [Leather]
Note: Increase the damage if is attacking from the enemy's back.

Porcupine (Level 11, 13, 18)
Golden Ape (Level 43, 53)
Triguatar? Man-horse (Level 61, 63)