If I am using Azir legend, and I have a Fiora, Worthy, 1 BF Sword and 1 Doran's Shield on the field, and I play Arise! to play 2 Sand Soldier unit tokens, can I equip the BF Sword to 1 Sand Soldier first, making it a Mighty unit, spend 1 power cost to ready it, and then equip the same BF Sword to the second Sand Solider unit, and making it another Mighty unit and spend another power cost to ready it as well?

Yes — the sequence works and Fiora, Worthy triggers separately for each Sand Soldier as it crosses 5 Might, but the two "ready it" payments accomplish nothing, and only one of the soldiers is Mighty at a time.

B.F. Sword's +3 takes a 2 Might Sand Soldier to exactly 5, which is Mighty, so Fiora's trigger fires (each trigger's [C] on an Order card = 1 Order power). Do the first attach with that token's Weaponmaster play effect (its Equip cost has no [A] component, so no discount — you pay full 1 Order power), then once Arise! and the resulting triggers finish resolving you're back in your Main Phase in an Open State, so you can activate B.F. Sword's Equip ability again and move it to the second soldier — Equip is just "[cost]: Attach this gear to a unit you control" with no once-per-turn limit (Rule 818.1.c.2). That drops the first soldier to 2 Might (no longer Mighty, and nothing triggers on losing it) and makes the second one Mighty, triggering Fiora a second time.

The catch is the readying itself: tokens are played ready, and nothing here exhausts them, so "ready it" does nothing (Rule 416.1.c). You'd spend 1 Order power per equip plus up to 2 Order power on the Fiora triggers for no actual benefit — and if the goal was two Mighty soldiers simultaneously, one Sword can't do it (Doran's Shield's +1 only gets the other one to 3).