First find the animals, then their sounds.
Puzzle:
"Exist!" I declare. (6)
Pee before run (8)
Crime boss be legend (6)
Fight? Aye, fight! (7)
Fine-ass software connector (5)
Gee, standard decay (6)
John Jay sample size (4)
Mug is not out (5)
Not from our commercial (4)
Oh, perhaps Jennifer's active (5)
Scratch off perfect score (6)
See iron file (6)
Stylish Barbie's boyfriend tee (7)
You and I are wicked (6)
You bottom, at the moment (6)
F W S D / L M2 O C / M1 H T / A B P R
Solution:
Each clue contains an extra word that is the homophone of a letter (more or less). The remaining parts clue two words that can be put together to make an animal word.
Before | run, [pee = P] easily: ANTE LOPE
"Exist!" [I = I] | declare.: BE AVER
Stylish | Barbie's boyfriend [tee = T]: CHIC KEN
Crime boss [be = B] | legend: DON KEY
[see = C] iron | file: FE LINE
[oh = O], perhaps Jennifer's | active: HER ON
John [jay = J] | sample size: LOO N
Scratch [off = F] | perfect score: MAR TEN
[you = U] bottom, | at the moment: MIN NOW
Fine-[ass = S] | software connector: OK API
[gee = G], standard | decay: PAR ROT
Mug [is = S] | not out: ROB IN
Fight? [aye = I], | fight!: SPAR ROW
Not from [our = R] | commercial: TO AD
You and I [are = R] | wicked: WE EVIL
If we put these in alphabetical order by animal, we might note that these animals start with the letters given below the clue (the fact that there are two Ms might also give us a clue - these go in alphabetical order). Replace each with the letter homophone from its clue (e.g., F for FELINE would become C) to get the answer: CRIB JUST FOR PIGS