Here is the full list of all 44 Running Fable achievements.
Reach experience level 2
Reach experience level 5
Reach experience level 10
Reach experience level 15
Reach experience level 20
Get 5 trap points in a single round
Get 10 trap points in a single round
Get 15 trap points in a single round
Get 20 trap points in a single round
Get 30 trap points in a single round
Come first for the first time
Come first 50 times
Come first 100 times
Come first 150 times
Come first in “Verdant Plains”
Come first in “Frozen Heights”
Come first in “Muggy Jungle”
Come first in “Moonlit Woods”
Come first in “Chilly Dream”
Come first in “Golden Wilds”
Come first but get disqualified for using the shortcut in “Verdant Plains”
Come first but get disqualified for using the shortcut in “Frozen Heights”
Come first but get disqualified for using the shortcut in “Muggy Jungle”
Come first but get disqualified for using the shortcut in “Moonlit Woods”
Come first but get disqualified for using the shortcut in “Chilly Dream”
Come first but get disqualified for using the shortcut in “Golden Wilds”
Reach the “Verdant Plains” trophy in less than 1 minute.
Reach the “Frozen Heights” trophy in less than 1:20 minutes
Reach the “Muggy Jungle” trophy in less than 1:25 minutes
Reach the “Moonlit Woods” trophy in less than 55 seconds
Reach the “Chilly Dream” trophy in less than 1:10 minutes
Reach the “Golden Wilds” trophy in less than 1 minute
Win 1 match of 3 rounds
Win 5 matches of 3 rounds
Win 10 matches of 3 rounds
Win 15 matches of 3 rounds
Win 20 matches of 3 rounds
Win 25 matches of 3 rounds
Win 30 matches of 3 rounds
Win first place by trap points at any level without reaching the trophy
Use the shortcut in any level and fall asleep before a player comes first
Score 50 trap points in a single round
Unlock all hats and outfits
Collect all the achievements