Mythical beast besides setter (4)
I believe the answer is:
yeti
'mythical beast' is the definition.
'yeti' can be an answer for 'beast' (I've seen this before). I'm not certain of the 'mythical' bit.
'besides setter' is the wordplay.
'besides' becomes 'yet' (I can't explain this - if you can you should give a lot more credence to this answer).
'setter' becomes 'i' (the person that set the crossword).
'yet'+'i'='YETI'
Can you help me to learn more?
(Other definitions for yeti that I've seen before include "Bigfoot" , "Legendary Himalayan dweller" , "hirsute specimen" , "He's never had a successful Catcher" , "Creature of disputed existence" .)