Animal connect wall

I made a connect wall about animals:

tarsier         ascidian           aye-aye       

caecilian       diplocaulus        bird

marsupial       amphiuma           hagfish

fish            lamprey            mammals                                   

There are 4 categories containing 3 words each.

Category 1 hint:

A type of cap and gown

Category 2 hint:

any animal with a backbone

Answer

OK, my answer was getting long. If you want to see my other tries, look at the edit history. Here goes another shot!

nocturnal animals - marsupial, tarsier, aye-aye. chordates - hagfish, lamprey, ascidian. amphibians - diplocaulus, amphiuma, caecilian. vertebrates - birds, fish, mammals.

Now technically my second and fourth classes could switch some, since (

Despite not having a backbone, hagfish are considered vertebrates. Lampreys are vertebrates as well, if I remember correctly.

)