Getting the heat into the braid helps, if you have a small soldering iron it'll be a difficult job. I used a soldering station from Jaycar, they no longer sell this model, but it did the job well.
I have a similar soldering station (Also Jaycar) and i found that the standard fine point tip struggled to heat parts to allow good solder flow. They sell a wider surfaced tip which works a hell of a lot better.
FrankenLab Hand crafting guitars, because Death Rays are expensive.