if you see the last achievement it says.
Punk'd
Unlock 10 of the 13 Circus Achievements along with any Abusement Park achievement.
so yes the maps achievements counts
Summer Sideshow map achievements
Normal difficulty
Flea Circus
Win a Long Game on Abusement Park on Normal Difficulty.
Hard difficulty
Dog and Pony Show
Win a Long Game on Abusement Park on Hard Difficulty.
Suicidal difficulty
3 Ring Circus
Win a Long Game on Abusement Park on Suicidal Difficulty.
Hell on Earth difficulty
On Top of the Big Top
Win a Long Game on Abusement Park on Hell on Earth Difficulty.
Summer Sideshow Achievements
Ringmaster
Kill the "Ring Leader" (Circus Patriarch).
Sparing with a Master
Kill a Circus Gorefast with a Melee Weapon.
Assistant Homicide
Kill 2 Circus Stalkers with a Melee weapon to the back in one wave.
Seeing Double
Kill 5 Circus Crawlers with a Bullpup in one wave.
Clearing Clown Alley
Kill 5 Circus Bloats in one game.
The Big Hunt
Kill a Circus Scrake with a Crossbow.
Lifting a Dumbell
Kill a Circus Husk with a LAW.
Small Hands
Kill 3 Circus Clots in a wave with the Lever Action Rifle.
Elephant Gun
Land the killing blow on a Circus Fleshpound with a Pistol
Juggling Act
Drop 5 different Tier 2 weapons in one wave.
Windjammer Enthusiast
Survive 10 seconds after being screamed at by a Circus Siren on Hard or above.
Taking Down the Big Top
Kill 4 Circus Zeds in 1 ZED time chain with a Melee weapon.
Burning up the Midway
Kill 10 Circus Clots with a Fire-based weapon.
Punk'd
Unlock 10 of the 13 Circus Achievements along with any Abusement Park achievement.