So the way I did the grind for legendary orders for a chance to get it to turn into an exotic order was by playing trials. As of this reply I have acquired every exotic catalyst and fully progressed em all since about 2 weeks ago. Playing trials for me was the fastest method, after every match the legendary orders bar would fill about 10 to 15% along with orders completed while playing the activity. Upon getting a legendary order I would then go and complete it during the shuro chi cp, the preservation mission on the throne world (if you do not kill savathuns projection the adds spawn infinitely), or the moon at sorrows harbor. If I had gotten an exotic order I would then complete it at either of those locations, then after completion jump back into trials to then begin my farm for legendary orders. This by far I think is the best and most efficient method, keep in mind I would try my best to win the matches of trials because I was also trying to get the lighthouse run for a chance for the new ships, ghosts, and sparrows as well as the shaders for the 5, 6 or 7 win streak. If anyone has a better or faster method for farming for legendary orders please feel free to reply your method. As of this reply I feel my method is the most consistent and time efficient way. Best of luck on your grind for the catalyst guardians 🍻🫡

It doesn't guarantee you a catalyst, I've had 5 & only 2 gave a catalyst