What's the correct way to solder wires on that (LiPo) battery's terminals?
Soldering battery terminals is usually a bad idea anyways because the heating process of soldering tends to damage the battery near the terminals, but apparently on Li-Po battery tabs, there's special zinc solder to do so. See here for more info.

The standard way it's done is with a spot welder or ultrasonic welder which gets the heat in and out fast. The downside is that you only need a grand or two to buy one of those...