I trapped a nuisance Beaver last year in a Conibear. I tried skinning that thing, but after it had laid in that trap in the cold water for up to 20 hours, it was the hardest thing to skin I've ever seen.

Any skinning tips are appreciated.

They can be quite a challenge.
I offer two suggestions: 1.Use a very sharp, short thin blade knife. 2.Don't cut yourself.

Try this for starters - Trapperman Beaver Skinning pictorial or Louisiana Fur Advisory Council

Beaver aren't that hard to skin.....You can't pull the skin off like a coon. You have to cut it all off. If you are selling green, most buyers don't care if you leave a lot of fat on the hide......... One trick I do to keep the "beaver fleas" off me; I wear long sleeves, and cloth gloves when skinning, and spray my sleeves and gloves liberally with Raid bugkiller...........After a few dozen, they get easier to skin. Grant

What about leaving flesh on the hide?

More then one way to skin a beaver....clean skinning and rough skinning.

Clean skinning is a dangerous thing for those who are just starting out. That is because when you clean skin you are using a very sharp knife with a lot of short little knife cuts, and just one little mistake and you have a hole.

I think that for a beginer the best way is to rough skin and then flesh them. Make sure you have the correct equipment. You will need a saw or a shear cutter for the feet, a sharp but rounded knife to skin with, and a very good quality board and fleshing knife to flesh with.
Don't skimp on the fleshing knife. I recommend the Decker which costs about $60.00. If you buy one of the cheap fleshing knives all you will have is trouble. You need a fleshing knive that has one dull side and one side that is extremely sharp. You will use the sharp side for where you actually have to slice off flesh from the hide (the head and part of the back near the tail) and the dull side to push flesh off everywhere else.

Make sure you get a quality fleshing board. Make sure it is absolutely smooth.

Work a little piece at a time. Take your time with it until you get comfortable knowing what you are doing. Different parts of the beaver have different thicknesses of hide. You don't want to tear it, and you don't want to cut it.

And then of course you will need boards to nail the hide. Or you can also use an electric staple gun if you don't want to nail. Make sure and do not overstretch. Buyers can see whether beaver hides are overstretched and they will dock you if you overstretch.