Dampen a sponge with water. Then heat up the soldering gun and wipe off the tip with the sponge. Apply tip tinner to prevent oxidation. Once the tip is bright and shiny, it's ready for soldering.

You need to heat up the entire shield and the pins at the same time, which the wire acts as a thermal gateway for. As long as there are melted solder bridges ... have a hot air gun or a hotplate ...