This is one of a series of guides for 104% completion of the current version of APICO (4.2.1). This specific guide covers the requirements for unlocking all 27/26 butterflies.

My other APICO guides:
Social Bees
Solitary Bees
Flowers
Fish

To bee perfectly honest, I don't know. "Chance" is a hidden stat that I found listed in the game files for bees, butterflies, flowers, and fish, but I have not been able to figure out exactly how it's used in the game. For butterflies, my guess would be it affects how likely it is that a butterfly will appear at any given moment when all necessary conditions are fulfilled. But that's just a guess. I have included the numbers because, at the very least, they do seem useful as an indicator of rarity even if I don't know exactly how they're being used.

Speckled Butterfly

• Time: Day
  
• Location: Forest
  
• Flower(s): Beekeeper's Delight, Butterfly's Friend
  
• Additional Conditions: N/A
  
• Chance: 40

Hypnotic Butterfly

• Time: Night
  
• Location: Forest
  
• Flower(s): Honeybriar, Honeysuckle
  
• Additional Conditions: N/A
  
• Chance: 38

Drizzled Butterfly

• Time: Day
  
• Location: Forest
  
• Flower(s): Swamwort, Stormwort
  
• Additional Conditions: Rain
  
• Chance: 39

Princess Butterfly

• Time: Day
  
• Location: Forest
  
• Flower(s): Honeyrose, Honeylip
  
• Additional Conditions: Nearby active beehive
  
• Chance: 32

Lesser Dreamer

• Time: Night
  
• Location: Forest
  
• Flower(s): Goldenrod, Bright Beacon
  
• Additional Conditions: Player must be asleep
  
• Chance: 36

Faded Butterfly

• Time: Night
  
• Location: Swamp
  
• Flower(s): Hivesbane, Ashthorn
  
• Additional Conditions: Nearby calmed beehive (either via a Smoker or an Empress Butterfly)
  
• Chance: 34

Marsh Skipper

• Time: Day
  
• Location: Swamp
  
• Flower(s): Beesknees, Flapjack
  
• Additional Conditions: Rain
  
• Chance: 28

Masked Butterfly

• Time: Night
  
• Location: Swamp
  
• Flower(s): Pondshine, Mothlight
  
• Additional Conditions: N/A
  
• Chance: 27

Painted Leaf

• Time: Dawn, Dusk
  
• Location: Swamp
  
• Flower(s): Lilypad
  
• Additional Conditions: Rain
  
• Chance: 25

Ocean Gale

• Time: Day
  
• Location: Coral Reef
  
• Flower(s): Ebbsquill
  
• Additional Conditions: N/A
  
• Chance: 27

Stippled Butterfly

• Time: Night
  
• Location: Coral Reef
  
• Flower(s): Sea Cauliflower
  
• Additional Conditions: N/A
  
• Chance: 32

Thorny Butterfly

• Time: Dawn, Dusk
  
• Location: Coral Reef
  
• Flower(s): Tidewort
  
• Additional Conditions: N/A
  
• Chance: 29

Reef Skipper

• Time: Day
  
• Location: Coral Reef
  
• Flower(s): Shipsbane
  
• Additional Conditions: Rain
  
• Chance: 24

Spooky Butterfly

• Time: Night
  
• Location: Swamp
  
• Flower(s): Willowisp (obtained randomly through breaking tombstones during the Hallowbeen seasonal event)
  
• Additional Conditions: N/A
  
• Chance: 24

Glacial Butterfly

• Time: Dawn, Dusk
  
• Location: Tundra
  
• Flower(s): Honeydrop, Royal Trumpet
  
• Additional Conditions: N/A
  
• Chance: 28

As was noted in the comments, despite what the wiki says, this butterfly does not seem to spawn when it's snowing. Both Sto's Journal and the game files seem to confirm this. Thank you, marketcve, for pointing that out!


Smoldering Butterfly

• Time: Day
  
• Location: Tundra
  
• Flower(s): Frosteria, Frostips
  
• Additional Conditions: Nearby active incense burner
  
• Chance: 24

White Tempest

• Time: Night
  
• Location: Tundra
  
• Flower(s): Beewell
  
• Additional Conditions: Snow (i.e. at the same time that it's raining in the Forest biome)
  
• Chance: 22

Since it does not normally rain or snow at night, you will need to use the Polar Idol to pray to the Hivemother at night and cause it to snow.


Antique Butterfly

• Time: Any
  
• Location: Underwater (Diving Spot)
  
• Flower(s): Saltwave
  
• Additional Conditions: N/A
  
• Chance: 22

Corroded Butterfly

• Time: Night
  
• Location: Underwater (Diving Spot)
  
• Flower(s): Claybriar
  
• Additional Conditions: N/A
  
• Chance: 25

Sunken Admiral

• Time: Night
  
• Location: Underwater (Diving Spot)
  
• Flower(s): Kelp, Algae
  
• Additional Conditions: Full moon
  
• Chance: 20

You can check to see what the current moon phase is by using Tom's Pocketwatch. A symbol representing the current moon phase will also appear in the top left corner of your UI at night.

Anointed Butterfly

• Time: Day
  
• Location: Hallows
  
• Flower(s): Hivanium
  
• Additional Conditions: N/A
  
• Chance: 20

Honeyed Greytail

• Time: Night
  
• Location: Hallows
  
• Flower(s): Honeycore Stalagmite
  
• Additional Conditions: N/A
  
• Chance: 18

Sunset Butterfly

• Time: Dawn, Dusk
  
• Location: Hallows
  
• Flower(s): Mothlight
  
• Additional Conditions: N/A
  
• Chance: 24

Lost Butterfly

• Time: Day
  
• Location: Underwater Cave (Underwater Diving Spot)
  
• Flower(s): Honeycore Stalagmite
  
• Additional Conditions: N/A
  
• Chance: 20

Greater Dreamer

• Time: Any
  
• Location: Hivemother's Dream
  
• Flower(s): Hivemother's Door
  
• Additional Conditions: N/A
  
• Chance: 16

The Hivemother's Dream is unlocked by unlocking the four Hivemother Gates in the main world, one in each Biome. Four of the Idols can be found in Shrines next to the Gates, the fifth can be purchased from the Merchant that spawns at night, and the sixth can be obtained as a reward for completing the Apiarist's Almanac.


Buried Empress

• Time: Night
  
• Location: Underwater Cave near the Green Emerald Coral Reef (east of the Hallows biome)
  
• Flower(s): Perpetunia
  
• Additional Conditions: N/A
  
• Chance: 15

Bugged Butterfly

• Time: Any
  
• Location: Dev's Hideout
  
• Flower(s): Debugger2 (command console item inside the house)
  
• Additional Conditions: N/A
  
• Chance: 30

(After unlocking three Hivemother Gates, the player has a chance of teleporting to and permanently unlocking the Dev's Hideout when using a Gate to teleport.)