The museum begins with very few monsters. As you bring monsters back from your travels, they get added to the collection. Be sure to grab two of every monster you find! One will go into the museum and the other will be in case the monster collector guy wants that one.

Here are the completed exhibits.

left room behind jewel guy
skeletal axeman
half brute
slim burble
goofy lizard (get in trade for 3 competition medals)
cobra
OPEN
squirt
cyclops
sea turtle
smiling burble
spitting toad
big bull
Geb
Spinefish

back room rat (from shop)
mummy chihuahua
armadillo - fire and electric
skeletal spider
nose needler
shell critter
mummy worm
wasp spider
spike spider
exo-piranha
OPEN
mummy eagle
OPEN
tree creature
small frog
alert spider

room behind animal guy
electric eel
chichuahua
green giant worm
blade scorpion
manta ray
shuttlecock bird (from shop)
featherless turkey (from shop)
mummy bird
knives cat
carbhands
sharpbeak
skull worshipper
skull swordsman
dark worshipper

Sphinx and the Cursed Mummy Walkthrough

Sphinx and the Cursed Mummy Review