You can do this mission the easy way or the hard way.
The hard way: Play this mission just like any other one on one missions. The thing is, you'll miss the movie sequences if you play like this.
The easy way: Remember how it all went down in the anime series? Defend yourself all the time and let the Angel grab you three times. I know it sounds crazy, but bear with me. After the movie sequence, your synchro ratio increases dramatically and the Angel's AT Field is destroyed. Now it's easy to fight this thing. I suggest the usage of grab attack. It'll do nice damage to the Angel.
Again, you can do this mission the easy way or the hard way.
The hard way: Play this mission just like any other one on one missions. You'll miss the movie sequences if you play like this.
The easy way: Let the Angel grab you from the leg and throw you away. The timer will start and you'll have a knife in your hand. Once you regain control, do NOT attack the Angel. Instead evade its attacks for 4 minutes and, if you want, destroy the Angel's AT Field. It will be hard thing to do, but it'll make this easier. Once the timer goes red, meaning you have only 1 minute left, press A and B at the same time, to do the grab attack near the Angel. The Angel dies no matter how much energy it has. You'll also see all of the movie sequences this way. Either that or you can try and kill the Angel normally (but you won't see the final movie sequence that way.)