Most reliant method to me seems to be:
1) Save up Card Reveals. Always keep 10+ of these for event gachas, but any above that can be used for this mission
2) Play GHQ behind the Extras button. This seems to be the place with the highest chance to spawn tripple chance rolls. It costs 20 stamina, but winning rolls are really more common per stamina used here.
3) Use Card Reveals on five stepups and SR Guaranteed tickets, but *only* when already found 1-2 SR cards randomly while on this mission.

2-3 times a week I clear it, and then the rest of the missions will often follow, depending on whether I have enough time left to play, lol.