My phone was acting up. Randomly restarting. A Google inquiry led me to believe that the battery was the problem. It was charging to about 80% of capacity.
After watching the video and reading the step by step instructions a couple of times I felt confident about the repair.
I read in the comments about some people using a warm rice bag to help with the removal of the adhesive under the battery. This seems to be a possible trouble spot in the process. So after lifting the screen up and I used a rubber band to hold it against a big ketchup bottle. I then put the warm rice bag under the back of my phone and proceeded to to remove the screws and cover. Then I popped the connector off and was ready to remove the adhesive strips under the battery. Once I was able to get ahold of them with my fingers I pulled as level as I could with constant pressure. I had to regrip a couple of times as it stretches as your it pulling out. Both sides came out with no problems.
I attribute this to the warm rice bag under the phone. In my opinion doing this before you have problems makes it much easier. The phone wasn't on the rice bag for more than 5-7 minutes before I removed the strips. This was the step I was most worried about as I'm sure I would have had to remove the screen from the phone if one or both strips didn't come out as they should.
Everything else after this point was all downhill for me. Just make sure you bend the battery connector so it lines up correctly before replacing the new battery.
1. Use a warm rice bag under the phone to warm the adhesive under the battery before trying to remove the strips.
2. Bend the battery connector on the replacement battery using the old battery as a guide.
3. I wouldn't take the screen completely off unless the adhesive strips don't pull out.