Instructions
Walk up the dark mass at the back of the room to start the battle with Leviathan. Back up until you're about halfway between Leviathan and the entrance to give yourself some maneuvering room. It will sprout three tentacles instantly to attack you, and each tentacle has a mass of yellow flesh that is its weak spot.
Shoot at the weak spot of the tentacle as it appears. The Leviathan will only show one tentacle at a time and it will keep shifting between them. If you see a tentacle slam to the ground, jump up out of the way, as it is getting ready to sweep the floor to attack you. Keep shooting at the weak spots as they appear until you destroy one of the tentacles.
Dodge the explosives that the Leviathan shoots at you every time you destroy a tentacle. Use Kinesis to throw an explosive back at the Leviathan. This will cause it to either bring out its tentacles again or resume shooting explosives at you, so plan your attacks accordingly. Continue shooting the weak spots on its tentacles and throwing explosives back at it until it is defeated.