You need LOTS of heat for the metal tabs connecting to the module; the reason being that the tin (and all the copper on the circuit board) steals alot of it. So, you're gonna need a 35 watt iron at least for this part (desoldering the 5 connector pins will be much easier).
Also, you CAN use the heat-the-board-up-n'-bang-the-solder-off trick, if you're careful. The idea here is to get the solder in molten form, and bang the board to the side (instead of down), so the solder runs across the board. Note that the solder holes for securing the tin module are not plated through, and there is never solder on the bottom side, so this trick will work, but it should be used as a last resort (i.e., as opposed to a "solder sucker"; don't even bother using braid for such alot of solder).
Finally, after you remove the module, in order to use the video signal, you will have to connect the base of an NPN transistor to the raw video out signal (collector to +5VDC, emitter will be your video out). This transistor reverses the effects that the PNP transistor (inserted earlier in the video out circuit) has on the video signal (0.6 volt difference), and also buffers the positive drive current to make driving a 75 ohm load (standard composite input load) possible. VCRs usually don't offer this load to composite signals, and the NPN transistor won't work properly. To circumvent this, place a dummy load on the video output (between the emitter of the NPN xstr & ground of the NES; use 470 ohms (or so) for the load).