Canst thou draw out leviathan with an hook?
or his tongue with a cord which thou lettest down?
Job 41:1
The key to understanding Job 43 and Leviathan is to read the whole chapter; the key verses are the last two.
Job 41:33-34 Upon earth there is not his like, who is made without fear. 34He beholdeth all high things: he is a king over all the children of pride.
So first, it is not speaking of anything upon the earth. With that it should be easy to see whom it is that it is speaking of.
Isaiah 27:1 In that day the LORD with his sore and great and strong sword shall punish leviathan the piercing serpent, even leviathan that crooked serpent; and he shall slay the dragon that is in the sea.
Revelation 12:9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.