If this is your own personal amp, replacing the single TIP102 may be acceptable but if you do this for a paying customer, you need to replace all of the transistors that are operating in parallel. In this case, you should have replaced all 3 of the 102s in that channel. Having matched components increases reliability.
A good soldering iron, a good desoldering pump and good quality desoldering braid is all you need to desolder most components. I like the WES51 iron. The edsyn DS017 is the best desoldering pump I've used. Chemtronics Chemwick braid is the best I've used.
For times when you need to work on sensitive boards you need to use special solder. ChipQuik solder is a low temp alloy that allows you to remove components at very low temperatures. This helps prevent damage to the board. It's most effective if you have a variable temp soldering iron. If you don't have a low/variable temp iron, you can apply it quickly with a hot iron and then use a heat gun to desolder the components.
it's a fun hobby though