Soldering Tiny Leads?
Flux! Use plenty of flux and it will magically work.  

You don't need:


a super-skinny soldering tip
hot air station
very thin solder
solder paste
desolder braid (helpful though)


You do need:


Flux
Magnification (you've got that covered)


Flux up the pads really well, then apply heat and solder.  Try to make a big ball that covers all the pads.  Then remove solder by repeatedly cleaning the tip and touching it to the pads.  This technique is similar to drag soldering.  If in doubt add more flux.