With a nearly maxed Water team and a useless Soul and EX ability (Arthur + Provisional Forest), I was able to auto-battle clear all the way to the last stage today. Clearly ability to clear is mostly a matter of equipment, good characters, and whether you have access to a +100% friend eidolon.
Elemental advantage is a big boon, and will likely impact whether you can reach the 3 and 5-orihalcum tiers. On the flip side, you shouldn't actually NEED the extra 3 orihalcum unless you're running more than 2 elements. 4 orihalcum a month (2x 2-orihalcum tier) should be plenty to feed teams for 1-2 elements and keep them maxed, and as an added bonus you won't need to bother with the challenge objectives.
By my rough calculations, you need about 1 orihalcum per element per month for weapon final limit breaks (Advent and Union event weapons). Clearing Guild Orders doesn't seem to be necessary if you're focusing on 1-2 elements. The 2-orihalcum tier allows you to gear 3-4 elements or limit break some Gatcha weapons. You'll need to reach the 3-orihalcum tier to gear all 6 elements, and the 5-orihalcum tier if you want to also limit break Gatcha weapons.