You'll face the Leviathan at the end of Chapter 6.
There are three waves to this boss fight. First, he attacks with three tentacles, the same ones that have attacked you earlier in the game and tried to drag you away. Same strategy applies here. Wait for the tentacles to extend, and fire away at the large yellow growth near the Leviathan's body until it explodes.
The second wave is a volley of pods from his "mouth." Move Issac up closer to the Leviathan to catch the pods with Kinesis and fling them back (With the Right Trigger) into its mouth. Doing this will unlock the Playing Catch achievement as well. You'll need to learn to time your Kinesis captures based on how long a range you have. Grab at the pod too early and you won't have a chance to grab it again and it'll slam into you; grab it too late, and well, it'll already have hit you. After a few explode in his mouth, (you'll know this because it cringes and closes it's mouth for a moment), you'll move onto the third wave.
The third wave is a combination of the first two, with pods being fired randomly at you while the tentacles attempt to crush you. Sometimes in this wave, the tentacle will slam down a distance from you, then sweep across the floor over you. Time it right, and you should be able to Zero-G Jump to a different area and avoid damage here. After you destroy all the tentacles, you'll be faced with just the pods flying at you, albeit at a faster rate than before. Repeat the strategy from the second wave a few more times and you'll finally defeat the Leviathan and get the unlock.