1st Encounter: The best way to defeat Carnage here is to jump on the two giant engines in the area. When he jumps at you (Spider Sense shows you when) jump away. Now quickly use to kick him into the engine. Keep doing this, and he will change up his pattern and jump off right away before you get a chance. You'll eventually knock him in enough to defeat him.
Final Encounter: There are two phases you will be rotating through. One of them is protecting the big guys with the flame throwers. Once they have burned through some life, Carnage will go back into regular form and attack you. You must dodge constantly and attack with or anything else you see fit. He is hard to dodge and it's hard to distinguish sometimes when it's safe to attack. He will grab you sometimes and drain your life. You must hit as fast as you can to get out. Once you've had his symbiote shield burned about 3 times, you will have defeated him.