I don't know a whole lot about console modchips, but I do know a bit about soldering. When soldering pins on most ICs (chips like this modchip) there are a few basic things to keep in mind.
While you would be best off with a smaller-than-average tip and variable heat, you should be able to pull it off with a standard one, so long as the tip isn't too fat/dull to only touch one pin at a time. When soldering ICs you need to make sure as little heat gets to the chip as possible, as too much can destroy the chip. Make sure you use solder with a high tin to lead ratio; more tin means it melts faster, meaning less time for heat transfer. A heat sink clamp can help, but isn't essential if you have a decent amount of soldering experience. If you need to desolder anything make sure you've got some solder wick (or even better, a "solder sucker" like
this one) to draw off the old solder.