Tips from doing this once.

1. Make sure you have the right tools. T3 worked for me. But T3 was not the right torx size included in the free tools that came with the EZ30 battery kit I bought (Ebay vendor)

2. If you keep your Nexus 6 in a case and/or if it gets hot a lot in the past, then you will have very sticky cover removal, and possibly battery coil sticks as well. Be patient, and use plastic tools with sharp edges to get the initial ribbon edges, and slowly peel the rest.