Before fusing, make sure you are in a Full Moon and have the Miracle "Mutative Element" turned on. Both of these factors will greatly increase your chances of a fusion accident occurring. I believe I saw someone do the math out there and it came out to a bit over a 50% chance of a fusion accident occurring, so it's worth preparing this way because luck might not be on your side.

Also be sure to save before this! It can get expensive!

To get Amabie, I fused together a Mandrake and a Quetzalcoatl.

To get Hare of Inaba, I fused tgoether an Aeros and a Mokoi.

For Kinmamon, try and fuse together the cheapest level 68-70 Demon you can manage. I tried various Demon fusions to try and make it cheaper and I couldn't settle on any single combination.