It depends what predators you are talking about.
if rats are a concern, or if you want to be very careful that weasels don't get in, then yes, hardwarecloth EVERYWHERE ON ALL SURFACES (including top) is by far your best bet.
Frankly though it is real hard to keep out determined rats or weasels, and it only takes one little opening, so an awful lot of totally-hardwarecloth-everywhere runs are not honestly nearly as 100% safe as their owners THINK.
If you are willing to take a little bit of a chance with rats and weasels -- which I think is totally reasonable if neither is a huge problem in your area and the chickens are always shut up in a secure coop at night -- then another perfectly good option is to use a larger mesh wire for the run, like HEAVY GAUGE 1x1 or 2x4 wire mesh, or heavy gauge chainlink, and add hardwarecloth to the bottom 3' or so of it. It is really important to use a stout gauge of wire, though - the lighter weight 'garden fencing' type wire mesh, and cheapie chainlink, are not going to hold up so well to a raccoon or dog or coyote.
Good luck, have fun,
Pat