Applying some solder flux to the jack terminal before soldering helps with heat transfer and the task goes quicker.
You need enough heat, you shouldn’t have to dwell with the iron on the terminal. Soldering that joint should take a couple of seconds. Attach the wire to the jack terminal. Apply flux. Apply heat. Then the solder. Having a jig to hold the jack helps. You can mount the jack on a plate, a thin piece of plywood or a soft jawed vise.
You need enough heat, you shouldn’t have to dwell with the iron on the terminal. Soldering that joint should take a couple of seconds. Attach the wire to the jack terminal. Apply flux. Apply heat. Then the solder. Having a jig to hold the jack helps. You can mount the jack on a plate, a thin piece of plywood or a soft jawed vise.