You encounter Leviathan at the end of Chapter 6, he's a pretty straight forward boss. He'll start off by attacking you with his 3 tentacles, make use of the zero gravity to avoid these attacks and shoot at the yellow growth until they explode which will destroy the tentacle.
Once you've destroyed all of the tentacles the Leviathan will start to shoot pods at you, there are 2 methods to this stage, you can either shoot away at them so they explode as he attempts to spit them at you or you can use Kinesis to catch a pod and then fire it back at the Leviathan. If you use the second method you'll also unlock this achievement: Playing Catch in Dead Space
if you don't have it already.
Eventually the Leviathan will send out his tentacles again while he continues to spit pods at you. You can either take care of the tentacles like you did earlier in the battle or you can dodge them and continue to focus on damaging Leviathan. Once he's defeated the achievement will unlock!
An example of this can be seen in the video below!* Credit to RoosterTeeth for the video