Coinín
From Anglo-Norman conil, from Latin cunīculus (and in turn from Greek κύνικλος). A possible etymology put forward for κύνικλος says it might be derived from a word meaning “burrow”; but it is thought that the reverse, deriving “burrow” from “rabbit” seemed more plausible. This is similar to how leamhan was derived from Old Irish.
Note: Up to the 19th century, in English coney referred to the rabbit (same etymology), and the term "rabbit" only referred to its young.
Dobhareach
The hippopotamus' name was derived the same was it was in English—hippos(horse)+potamos(river). Dobhar(water)+each(horse). Each is an older name for a horse (we commonly see capall) and is related to "equine" and "equestrian".
Francach
The rat is also known as luchóg mór, but francach is literally "French", and it is popularly believed that they were first brought to Ireland from France. However, there is another possibility: Francach also refers to "foreign", "exotic" or "large", perhaps used in contrast with a mouse.
Giorria
The hare is literally called short deer, from the earlier girr-fhiadh, from gearr + fia(dh). It is purported that this is because hare, as opposed to rabbits, ran really quickly over the land rather than burrowing and was thus likened to deer.
Mac Tíre or Machtíre
Wolf, or son of the countryside. The etymology is unclear, but on RTÉ special Wolfland, it was said to be a euphemism and the original word could possibly be related to (or be) olc, which became taboo because it was associated with the horrors of the wolf. Another theory is that machtíre is considered to be half human.
Other words include madra allta (wild dog), faol (from the proto-Celtic waylos, howling one) or faolchú (faol + cú, hound).
Madra Rua
Also known as sionnach (Old Irish sinnach), the fox is literally “red dog”. It might show up as Madadh Rua in Connacht and Ulster Irish. It is also known as Loisinnán, or 'little white tipped one', for its tail.
Mathúin
More often béar from English, mathúin, from mathghamain, is a compound of maith + yearling calf or deer. It is also used as a name, anglicised to Matthew.
Sciatháin Leathar
Having only heard it as ialtog, I was beyond thrilled to find that the bat is also called leather wings. Even better, bás dorcha, or black death is also accepted. Say you wanted to go the cute route, you could also say eitleog (little flyer).
Srónbheannach
I was pleased to learn that the rhinoceros was, in Irish, nose horned.
Torcán Craobhach
Torcán "little boar" → torc (wild boar) + diminutive -án + craobhach (branches, branching, dendritic). A wild boar is thus a 'little branched boar'.