Here is the full list of all 27 Stickman Fighting achievements.
Win your first fight
Achieve the 2nd level
Defeat two enemies in a single fight
Activate Leg Strike and Arm Strike simultaneously
Activate Defense and Rage simultaneously
Activate Leg Strike, Arm Strike, Defense and Rage simultaneously
Complete the Dragon Gorge area
Purchase 5 Hats
Defeat the First Boss
Achieve the 5th Level
For 15 seconds from the start of the fight, don't receive and don't inflict any damage
Let the fight time reach the zero
Heal Yourself 10 Times
Complete the Cemetery area
Complete the Space Station area
Complete the City area
Achieve all stars in the game
Achieve the 10th Level
Purchase 5 pair of boots
Purchase 5 suits of armor
Kill 50 stickmen
Complete the Challenge Mode
Defeat 3 stickmen in a single fight with 100% HP remained
Heal yourself, while you have less than 10% HP remained
Win a fight with less than 5% HP remained
Totally explore the game world (complete the storyline and challenge modes and buy everything)
Purchase all equipment in the game