First of all, I would check with your tenancy agreement to see if you can even think about doing any of this without express permission. You never know.
If all is OK to proceed....fine.
If the mural wall covering has a smooth surface (it should do), why not try painting over it, as this would be by far the easiest option.
Choose a small, preferably discrete area (couple of square feet) and see how the paint takes.
You may need to give it a couple of coats (letting the paint dry for a few hours in between coats) to cover the bold pattern completely.
If it won't cover, then you know you have to strip it. If it does cover but makes the wall look lumpy with ripples, give it time to dry out thoroughly and look again, as painted paper sometimes does this but dries out smooth and flat.
In the UK, we usually soak the wallpaper and scrape it off the wall using a hand scraper. The long handled pro ones are best, but there are other varieties.
I tend to use one of these plant sprayers to wet the paper (with water).
Spray a test area of about a square foot to see if the paper has a porous surface. If it has a vinyl surface, the water will not penetrate, so you will have to strip this outer layer off first.
Most vinyl papers will gradually pull off in large chunks if you take care and peel it off slowly. The hardest part is picking away the first inch or two to get you started, so I hope you have good fingernails and patience.
Once you have any waterproof covering removed, the ordinary porous paper should scrape off easily once you have soaked it sufficiently.
Always watch out for light switches and electrical sockets, especially down below your area of soaking, as the water will run down there if you use too much.
Always line the floor at the bottom with some sort of protective covering to minimise possible water damage. There shouldn't be too much water, but the soggy paper will fall and lie there while you work.
I use plastic bin liners or similar, if there is a nice carpet or fragile flooring to worry about. Try not stepping in it as you work.
Afterwards, when the bare wall has properly dried, try running the palm of your hand over the surface to detect any rough spots, as these will stick out like a sore thumb when you paint it. Sandpaper (glasspaper in the US) as necessary.
You may also have to check for small defects (holes and cracks) as well, hidden by the wallpaper covering. Fill as necessary.
Personally I would try option A and paint over it. Modern day paints just about cover everything nowadays.