I remember landing at Nice once, looking out the airplane window waiting to disembark and seeing my monofin bag, with Fragile stickers over it, being frisbied into the suitcase trolley then having a suitcase thrown on top of it :vangry:vangry:vangry
It depends on your monofin bag. I have a bag that Howard Jones used to make years ago, tough silver material (same as the surfboard bags) - great for around London but you can't fit much padding in it. So I concentrate on covering the corners with lots of cardboard (if the bag bends it'll bend at the corners), then cram it into the mono bag, then stick in some 1-2 inch thick styrofoam along the bottom edge of the mono, both top and bottom sides, then stick in as much cardboard, bubble wrap and styrofoam as it'll fit in before zipping it shut. It's an incredibly tight fit and I always struggle to repack it when I have to leave but so far (touch wood) it's got me to plenty of places around the world.
The main thing to think of, is that they'll throw it around (so protect edges), they'll throw things on top of it (so pad out top and bottom) and they'll throw sharp edges on it, like wheels of other bags and handles etc (so pad it out enough so that there's no surface touching the bag itself.
The footpockets are usually ok to leave unwrapped as they're only rubber.
If you have a bigger bag such as a Waterways or Leaderfins bag then I used to put styrofoam all around the top and bottom of the blade, bubble wrap it all, place cardboard over the top and bottom of the blade then tape it all up very tight.
Make sure you take some packing tape with you on your holiday too, so you can do it all up again at the end!
The mono's can take a bit of bend at the end, but it's the edges you really need to protect and the chance of puncture from a wayward suitcase and/or baggage handler.
Hope that helps.
Cheers,
Ben