Do some practicing with other things first. A few things:

- As someone pointed out, you may have lead-free solder, which has a higher
melting point. But you should use it for the repair, since the connector
probably has the same stuff already on it.

- There may be an invisible coating on the soldering iron tip, or it may not
be properly tinned. The last couple of mm of the tip should have a coating
of melted solder, applied by you.

- Some coaxial connectors have a nickel (?) coating that is hard to solder.
Using fine sandpaper on them really helps, as does a rotary wire brush.

Your soldering iron looks fine (low-end, of course). Is the tip tightly
attached? Try loosening and retightening the screw while it is hot (use
care).