Get a hemostat (looks like a very skinny needle-nose pliers, usually stainless steel or chrome-plated). You can sometimes find these at a hardware store or tool supply house; otherwise a medical supply vendor.
Remove the battery from the Gameboy and keep one finger on the - battery contact inside the battery compartment. This will protect the unit from static electricity damage from the other hand holding the hemostat. Use that tool to carefully straighten the bent pins. Bent pins break easily; that's why you need to be careful not to use too much force or bend them too far the other way.
If you do break a pin, you'll have to replace the connector. This requires some fine soldering skills and good tools. It is not something you can do with Grandpa's soldering gun.