Here is the full list of all 18 Animal Rescuer: Prologue achievements.
Save a Hellenic Hound with red-sign
Save a Cat with red-sign
Save a Cattle with red-sign
Save a Wolfhound with red-sign
Save a Chick
Save a Chicken
Save a Sheep with red-sign
Save a Horse with red-sign
Save a Rat
Save a Snapping Turtle
Save a Box Turtle
Save a Doe with red-sign
Save a Goliath Spider
Save a Pike
Save a Perch
Save a Camel with red-sign
Save a Fox with red-sign
Save a Stag with red-sign