It can be done with either
Does this mean I need 4 relays.4 in-line fusesand 2 ground wires all coming from the battery? Oh and what amp fuse?
2 or 4 relays. If you use 2 then the relays, wires and connectors will need to be twice the capacity, of course. And if you run 4 wires then each can get smaller.
However, remember that the high and low beams are not on at the same time, so you really don't need separate runs for each, the same wire can power both relays, since the load will not be doubled.
Personally, if I was to wire this from scratch, I would use 1 large wire (well, 2 really, one for hot and one for ground), run it to 2 relays, then run the post-relay output to both headlights. It's just simpler and as long as you size everything correctly, there is not a problem with this.
As far as sizing everything, there are charts on the internet that show what size wire can carry what kind of load. It's a triad between volts and watts and amps. As I recall, a high beam halogen headlight pulls 55 watts and a low beam something like 45. So 55 watts at 12 volts is 4.6 amps draw, x 2 for both headlights. A 12 gauge copper wire can handle around 20 amps, so that will be fine with plenty of spare capacity. And most automotive relays are in the 20 to 30 amp range, so that will be fine too.
But resistance usually occurs at the connectors, not at the wires, so make sure you use quality connectors that are corrosion resistant and properly sized. As to whether to solder or not in automotive applications, that appears to be a subject of much debate - I'll leave that one to you.
Pete