Wong,
I can't really tell from the picture, but I would assume that the shackle itself tapers along the length. Thus, when you grip it in the vise, you only get a line of contact with the vise jaws which makes it easy for it to tip this way and that. That is compounded by the swing-latch closure riveted on (which I am sure you do not want to remove.) Were you to scribe lines a given distance apart approximately perpendicular to the ring line, you could measure the thicknesses and find the included angle. Halve that and make a tapered shim set. You should then be able to clamp it in your vise.
It may be an optical illusion, but the top photo appears to show a "dimple" on the end of the swivel-ring base. That does not appear in the middle photo (and not visible one way or the other in the bottom photo). If that is there, it should help you center up your drill bit. If not you will want to use a centerdrill or a spotting drill to start your hole. A regular drill bit wll do its best to "walk" on such a surface. If you have access to a milling machine, that would help as: (A) you can dial in to center on the base of the shackle and (B) the spindles are many times more rigid than is common for drill presses.
I hope this helps.
