Here is the full list of all 88 Animal Rescuer achievements.
Save a Hellenic Hound
Save a Cat
Save a Cattle
Save a Wolfhound
Save a Chick
Save a Chicken
Save a Sheep
Save a Horse
Save a Rat
Save a Snapping Turtle
Save a Box Turtle
Save a Doe
Save a Goliath Spider
Save a Pike
Save a Perch
Save a Camel
Save a Fox
Save a Stag
Save a Snake
Save a Tiger
Save a Salmon
Save an Eagle
Save a Scorpion
Save a Wild Boar
Save a Domestic Pig
Save a Pig
Save a Goose
Save a Bat
Save a Komodo Dragon
Save a Pug
Save a Goliath Grouper
Save a Leopard
Save a Rhino
Save a Crow
Save a Buffalo
Save an Octopus
Save a Tucano
Save a Bear
Save a Longhorn Cattle
Save a Highland Cattle
Save a Mackerel
Save a Redeye Bass
Save a Fire Salmander
Save a Shark
Save a Zebra
Save a Crocodile
Save a Lizard
Save an Ibex
Save a Goat
Save a Wolf
Save a Frog
Save a Rabbit
Save an African Elephant
Save an Asian Elephant
Save a Crab
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 Sheep with red-sign
Save a Horse with red-sign
Save a Doe with red-sign
Save a Camel with red-sign
Save a Fox with red-sign
Save a Stag with red-sign
Save a Snake with red-sign
Save a Tiger with red-sign
Save an Eagle with red-sign
Save a Wild Boar with red-sign
Save a Domestic Pig with red-sign
Save a Pig with red-sign
Save a Komodo Dragon with red-sign
Save a Pug with red-sign
Save a Leopard with red-sign
Save a Rhino with red-sign
Save a Buffalo with red-sign
Save a Tucano with red-sign
Save a Bear with red-sign
Save a Longhorn Cattle with red-sign
Save a Highland Cattle with red-sign
Save a Zebra with red-sign
Save a Crocodile with red-sign
Save a Ibex with red-sign
Save a Goat with red-sign
Save a Wolf with red-sign
Save a Rabbit with red-sign
Save an African Elephant with red-sign
Save an Asian Elephant with red-sign