Here is the full list of all 37 Red Head - there are To The Rescue achievements.
Access for the first time Green Valley
Access for the first time Scalding Desert
Access for the first time Abandoned Mine
Access for the first time Ice Land
Access for the first time Magmariam
Access for the first time Sorcerer's Lair
Defeat Ancient Tree
Defeat the Great Sphynx
Defeat Crystal Spíder
Defeat the Snow King
Defeat Volkanon
Defeat Vamoth the Dark Sorcerer
Defeat the Ancient Tree without taking damage
Get 3 Sphinx riddles right
Complete Abandoned Mine without use light power-up
Collect all coins from Ice Land
Kill all enemies in Magmariam
Collect all diamonds of Green Valley
Collect the heart and papyrus of Green Valley
Collect all diamonds of Scalding Desert
Collect the heart and papyrus of Scalding Desert
Collect all diamonds of Abandoned Mine
Collect the heart and papyrus of Abandoned Mine
Collect all diamonds of Ice Land
Collect the heart and papyrus of Ice Land
Collect all diamonds of Magmariam
Collect the heart and papyrus of Magmariam
Collect all diamonds of Sorcerer's Lair
Collect the heart and papyrus of Sorcerer's Lair
Collect all diammonds
Collect all hearts
Collect all papyrus
Sleep
Access for the first time The Bridge
Collect all diamonds of The Bridge
Collect the heart and papyrus of The Bridge
Kill a rainbow fish in the secret location of The Bridge Stage