With Staff, the combo with Rifle named Flip Burst Mastery has two combos available for that one move. Tap Hold Hold works fine, combo-ing into the rifle attack Tap Tap Hold Hold does not combo into a rifle attack at all.
The other one should be Tap -> Hold -> Hold -> Hold. Tap -> Tap -> Hold should go into a standard Staff combo (can be followed up by another Hold if you want). The ranged one is Hold -> Hold (directional of not).
To add to this, Mortar Mastery goes straight to hold, hold range. It should be Hold, Flick analog, Hold. No flick of the analog is necessary to make it work