Currently, I'm looking at another asteroid, which may be harder to get to than 3554 Amun. It is called 1986 DA, and it appears to be very similar to Amun. The physical breakdown and mass of the asteroid appears quite similar. Another $20 trillion asteroid.
It looks to me like you could land on it. It has a rotation period listed, which indicates a turning speed of about 1 kilometer per hour. You could match that speed and hover over its surface. The gravity would be minimal, so you wouldn't fall very rapidly towards the surface. A brief burst of propellant can keep you hovering while preparations for a firm landing are made.
To land firmly must take into account the lack of gravity. Things will want to fly off the surface, so care must be taken to keep things firmly planted. Hence the landing strategy. I suggest firing hot projectiles that will penetrate the surface for a sufficient distance and then cool down and solidify forming an anchor. Several of these below the hovering lander should be set before reeling in the tether and securely attaching the lander to the surface.
Once landed, how to begin mining operations? As mentioned, any movement is likely to want to send you flying off the surface, so a strategy for mining should take that into consideration. Once again, I suggest making the surface very hot so that it melts, then scoop it up. While it is cooling and before it cools too much, I'd spin it up. Platinum is more dense with a higher melting point than nickel and iron, which makes up the majority of the mass of the the asteroid. The spinning movement will send the platinum to the edges of the vessel. Skim this off to obtain the platinum. Before the iron and nickel cools down to solid form, shape the iron and nickel into something useful. You could use 3D printing for this purpose.
Where to get the energy for this? You could use nuclear reactors designed for space. There are those in the 400 kw range that may be sufficient for this purpose.
Would this method work? Perhaps not. I've never done this before. Except something like it in a chemistry lab in high school. The spinning device acts like a centrifuge. More massive stuff will go to the edges. That's how that method works. Heating metals? Well, I've seen that on youtube, so it isn't out of the realm to heat up the ore sufficiently for this to work.
Getting to the asteroid would be accomplished with a solar sail. Perhaps the entire thing could be done unmanned, but it would be cool to do it with a crew.
This will be a new series. Part II is here.