Best way to hand-solder this TQFP (SMD) component
Learn to use "drag soldering" technique. Basically, instead of trying to solder each pin individually, you just get a bead of solder on the tip and roll it across the pins. As you hit each one, it'll leave just enough solder on the pin to attach it.

A video will do a lot to help explain here:

https://www.youtube.com/watch?v=wUyetZ5RtPs

There's a few things that help make this work:


Apply flux - lots of it - before you start soldering. Yes, I know the solder you're using probably has a flux core, but that's not enough here. (If you use paste flux, the paste can also help keep the part in place.)
Using the right kind of tip helps a lot. A small tip is not what you want here! I use a Hakko "hoof" tip (T18-C2); there's probably equivalents for most other good irons.