This achievement will take quite a bit of time to finish. However, if you follow this video (credit to PowerPyx) you will finish it in relatively good timing. Here is the video:
Here is the timeline given in the comments:#1 - Gerbil - 0:05
#2 - Long-eared Hedgehog - 0:35
#3 - Four-toed Hedgehog - 1:05
#4 - Afghan Pika - 1:44
#5 - Common Raven - 2:17
#6 - Trumpeter Hornbill - 2:54
#7 - Black Stork - 3:25
#8 - Oriental Stork - 3:56
#9 - Jehuty - 4:55
#10 - Griffon Vulture - 6:02
#11 - Lappet-faced Vulture - 6:43
#12 - Martial Eagle - 7:33
#13 - Karakul Sheep - 8:08
#14 - Cashmere Goat - 9:00
#15 - Nubian - 9:44
#16 - Boer Goat - 10:35
#17 - Wild Ass - 11:14
#18 - Grant's Zebra - 11:54
#19 - Okapi - 12:35
#20 - Gray Wolf - 13:19
#21 - African Wild Dog - 14:08
#22 - Side-striped Jackal - 14:50
#23 - Anubis - 15:26
#24 - Brown Bear - 16:22
#25 - Himalayan Brown Bear - 17:19
#26 - Deathstalker - 18:47
#27 - Emperor Scorpion - 19:21
#28 - Oriental Ratsnake - 19:55
#29 - Black Mamba - 20:29
#30 - Tsuchinoko - 21:00
#31 - Rainbow Agama - 21:37
#32 - Namaqua Chameleon - 22:10
#33 - Leopard Gecko - 22:40
#34 - African Fat-tailed Gecko - 23:14
#35 - African Bullfrog - 23:49
#36 - Russian Tortoise - 24:25
#37 - Leopard Tortoise - 25:01
#38 - Bechstein's Bat - 26:15
#39 - Rock Hyrax - 26:50
#40 - Tree Pangolin - 27:24
#41 - Sand Cat - 27:55
#42 - Caracal - 28:28
#43 - African Civet - 29:01
#44 - Marsh Mongoose - 29:30
#45 - Red Fox - 30:01
#46 - Blanford's Fox - 30:29
#47 - Honey Badger - 31:02