As the 60at60 is including some overseas travel, the list contains animals local to the places to visit:
The Resplendent Quetzal
A visually remarkable bird of central America that was sacred to the Mayans and the Aztecs, and now is at risk of extinction due to habitat loss.
Managed to see one in Costa Rica, which required an early morning start.
The Tapir I was hoping to see this in Costa Rica, but despite a hot sticky day in the jungle seeking them out in an area they were known to be wild, a footprint is the closest we managed!
Sloth We managed to see sloths in a couple of places in Costa Rica, once in trees next to a supermarket car park, and this one from a boat on the Peninsula de Osa
Himalayan Blue Sheep Description from BBC Nature: Bharals are sheep whose coats have a bluish tint which makes them almost invisible against the rocks of the Himalayas. This vanishing trick, together with the ability to bolt and hide in the rugged cliffs, enable bharal to escape the snow leopards and wolves that hunt the area. Bharals have traits that come from both sheep and goats. The current view has them more closely related to goats, but with sheep-like traits. Partly the result of the inhospitable terrain they inhabit, numbers of bharals in the wild remain good Certainly agree with the blending in to the background and their agility over rough ground comments. We saw them in a number of valleys in Ladakh including Stok valley leading up to the Stok Kangri base camp.
Marmots I've seen marmots in France and Switzerland but I was hoping to renew the acquaintance in Ladakh and I wasn't disappointed.
Griffon Vulture I did have a Lammergeier on my original list, but very happy to substitute with a Griffon, seen on the ground and in the air.
Bonus from Ladakh The mouse hare or pika was a delightful animal seen in a number of valleys and especially prevalent on the Nimiling Plain.
Bonus from Cornwall Just sitting on the decking of the chalet we had hired for the week at Whitsand Bay Cornwall having a cup of tea in the autumn sunshine, when a stoat wanders into the vicinity. After stopping for a photo promptly despatched a rabbit we had not even noticed hiding in the bushes and swiftly dragged it off.