It is very important to lift it form underneath... The connector on the motherboard is very fragile.
Beware, I bought a spare battery and its connector was totally crap. I have no difficulty to plug the original battery, but the "not so original" battery has a very bad connector (big welds, plastic dock not well formed)
I would recommand to not unplug the antenna from the motherboard. When I tried to do it, the plug has been remove from the pcb because it is very fragile. And you can remove the screen, the battery without removing the antenna from the pcb.
The only problem I have now is that the "wake on screen double tap" doesn't work anymore and I don't know why.
That was the most difficult part to me.
The double sided tape is quite strong and was place on the right (the antenna cable side), so I had to lift the battery on the opposite side and then use a blade.
If you have the opportunity, you should separate the battery from the tape, I noticed that it was very easier than to separate the tape from the phone case.
Try to unplug the battery cable first. I think it is the blue one on top right, near the antenna connector
For an unknown reason, the phone didn't work at all at my first attempt.
Then I checked again the connectors to plug in back in step 5.
I removed the battery again in order to check all the connectors :
The one from the bottom is very easy to plug before putting back the battery in its place, because the cable must be push into the connector
In order to be sure not doing crappy thing, I suggest to unplug/plug the battery connector (I think it is the one on top right of the battery, near the antenna connection on top (it is writtent P+ and P- on the cable hidden side)
When I plugged in back this battery connector, the vibrator activated and the phone worked well.
I didn't have a heat gun nor a hairdryer but I managed to remove the screen... I was a little scary and I had to be less gentle than usualy : I cracked the screen and broke everything...