I've done hundreds of these.
Just learn to install SLIM SMD Battery Holders. This will allow you to use regular name brand CR2032 batteries, instead of the shitty Chinese ones with tabs. Then you only have to hit your board once with an iron. I've fit these in NES, SNES, GENESIS, MASTER SYSTEM, AND N64. Take note though that even though they always fit snes perfect, genesis is a tight fit, and for nes you will likely have to pull off a small plastic pillar inside the cartridge shell.
https://www.ebay.com/itm/HQ-SMD-CR2...854726?hash=item58d3855d06:g:MggAAOSw~otWg32G
Get a desoldering pump, the braids suck.
A Panvise Mini will serve you well.
https://www.amazon.com/PanaVise-Mod...&qid=1510903366&sr=8-1&keywords=panavise+mini
As far as other tools.
A super small screwdriver to pry the contact out of the bottom of the battery holder, so it fits in the pcb.
Something like needle nose pliers, to bend the other piece on the battery holder.
Paper tape is great, helps hold the battery holder in place while you solder it in.
Something to clean the PCB while you're in there, cause sometime they are kind of crusty near the battery tabs. I just use q-tips and alcohol, but probably not the best idea. Also, sometimes after soldering in a battery/battery holder you will want to clean around the solder points.
The main thing with installing battery holders, is that it takes a little practice to not break the holder. If you look at that linked auction, you will see the gold contacts. That bottom one can pop out, or you can bend them to far, and the gold part snaps off. Order extras. Once you get it down though it's easy. The hard part is getting the battery out (sometimes), and actually getting the holder in (sometimes). That really depends on how clean the battery tab slots on the PCB are after you desolder it. One tip I learned on getting the batteries out that are troublesome, is while you have the iron on the solder joint, use the needle nose pliers to pull the battery out at the same time. Sometimes they can be a pain in the ass.
In the case when you remove the battery, and the holder tabs don't fit in the pcb slots, throw a little more solder on there (after the battery is out), and use the pump and try and get all the solder out at once. It's kind of hard to explain, but sometimes the solder just fills the holes on the PCB you need to battery holder tabs to fit in, and it's a major pain in the ass (at least for me cause i'm not a professional), this is when you need to add solder, or else when you try to use the pump to suck it out, you won't make any progress.
It's also important to remember the solder rule. This may be slightly off, but I believe you only leave the iron on the board 3 seconds at most, and don't try again until you've waited 10 seconds. You don't want to overheat your board.
I'm sure some people will give you better tips, but this method has worked for me for years.