Some creatures are resistant to spells, likely including Avada Kedavra.
Yes, there are certain magical creatures that are resistant to spells, which likely would include Avada Kedavra. Many of the largest magical creatures, and ones with an XXXXX Ministry classification, are either explicitly stated to be resistant to spells, or are considered so dangerous to wizards that it seems unlikely that magic would work particularly well on them, since if spells were effective on them, they shouldn’t be so difficult for wizards to handle.
Erumpents:
The Erumpent’s hide repels charms, and is also specifically said to repel curses, which Avada Kedavra is classified as.
“Weighing up to a tonne, the Erumpent may be mistaken for a rhinoceros at a distance. It has a thick hide that repels most charms and curses, a large, sharp horn upon its nose and a long, rope-like tail.”
- Fantastic Beasts and Where to Find Them
Dragons:
Dragons are powerful, and very difficult to subdue with magic, so it’s likely that Avada Kedavra wouldn’t work on them - it may take multiple castings to work or may not work at all.
“There’s a way, Harry. Don’t be tempted to try a Stunning Spell – dragons are strong and too powerfully magical to be knocked out by a single Stunner. You need about half-a-dozen wizards at a time to overcome a dragon –”
- Harry Potter and the Goblet of Fire, Chapter 19 (The Hungarian Horntail)
Graphorns:
Graphorn hide is even tougher than a dragon’s and also repels most spells, so it’s also likely to be resistant to Avada Kedavra.
“Graphorn hide is even tougher than a dragon’s and repels most spells.”
- Fantastic Beasts and Where to Find Them
Manticores:
The Manticore has skin that repels almost all charms, and although Avada Kedavra isn’t a charm, it’s likely that Manticore skin repels other types of spells as well, which may include Avada Kedavra.
“Manticore skin repels almost all known charms and the sting causes instant death.”
- Fantastic Beasts and Where to Find Them
The Nundu isn’t explicitly said to be resistant to spells, but since at least a hundred skilled wizards are needed to subdue it, it’s very likely it is, since otherwise so many wizards would not be necessary.
“A gigantic leopard that moves silently despite its size and whose breath causes disease virulent enough to eliminate entire villages, it has never yet been subdued by fewer than a hundred skilled wizards working together.”
- Fantastic Beasts and Where to Find Them
Additionally, similar logic applies to other creatures classified as XXXXX - they’re not specifically stated as being immune to spells or magically powerful enough to resist them, but they likely are since they’re considered so dangerous to wizards - if spells were effective on them, it would be easy for a competent wizard to handle them, and they then shouldn’t have such high danger ratings. Presumably, if these creatures could be easily dispatched with a single Killing Curse, they would be considered much easier to handle.
Avada Kedavra does affect phoenixes, but does not kill them - instead, it causes their existing body to burst into flames and be reborn.
Avada Kedavra does not kill a phoenix, since when their body ‘dies’, they are reborn from the ashes.
“The phoenix lives to an immense age as it can regenerate, bursting into flames when its body begins to fail and rising again from the ashes as a chick.”
- Fantastic Beasts and Where to Find Them
As such, Avada Kedavra does have an effect on a phoenix, but instead of being killed, it will burst into flames (as it naturally would when it reaches the point where its body is failing) and then be reborn from its ashes as a baby phoenix.
“But even as he shouted, another jet of green light flew at Dumbledore from Voldemort’s wand and the snake struck –
Fawkes swooped down in front of Dumbledore, opened his beak wide and swallowed the jet of green light whole: he burst into flame and fell to the floor, small, wrinkled and flightless.”
- Harry Potter and the Order of the Phoenix, Chapter 36 (The Only One He Ever Feared)