How do I fix an N64 cartridge?

[The Shadow]

It's actually pretty easy, you just need to be able to solder the new one on.
Personally though, I would use the opportunity to install a CR2032 clip, so that the next time this happens, all you need to do is pop the battery out and pop the new one in.
https://www.ebay.com/itm/10x-CR2025-CR20...ctupt=true