1st Encounter: This is a pretty basic fight, just attack and dodge like you would on normal enemies. There are a few emblems to collect if you get low on life, or you can kill the enemies. You can ignore the enemies completely if you want to and still do fine in the fight. When he is standing still, he will have a prompt on him, but it;s a very light damaging move that you end up doing.
Final Encounter: There are now 3 Deadpools but they all share the same health bar. Each 1/3 of the bar you take down, one will be defeated. Use your + combo to get good range while they surround you, and make sure you dodge the attacks. Each Deadpool attacks differently based on what weapon they have, but in the end they are going to feel about the same as your first battle. There will be times when there will be exploding objects falling from the sky and you must keep climbing the fence to make sure you don't get hit by them.