Wavebouncing & B-reversing
Wavebounces, b-reverses, and turnarounds are performed during the startup of most characters' specials; Shulk’s own neutral special, the Monado Arts, is no exception. However, by virtue of its delayed startup (i.e. the Monado Art Activation or Art Lock for short) taking place 45 frames or 3/4's of a second after the final neutral special input (during cycling), these aforementioned movements are non-trivial to perform with Shulk's unique neutral special. We can consider this final neutral special input as “frame 1” of Shulk's neutral special, and it follows that the Art Lock occurs on frame 46.
Beyond the Art Lock (FAF 6, intangible) there is no hitbox, nor counter frames, nor inactionable frames of any sort hindering Shulk. This frame data then permits influencing Shulk's facing direction and/or momentum directly before performing other moves-- albeit in a premeditated manner. Optionally, Shulk can exploit the nine (9) subsequent intangible frames (i-frames) of an uninterrupted Art Lock animation (a.k.a. the Art Pose) which conclude on the same frame Shulk announces his new art's name (frame 60).
Doing a turnaround (or 'reverse b', rB) means influencing the special move's startup in order to flip a character's initial facing direction.
The window to input rB (which is accomplished with a stick-input opposite to Shulk's initial facing direction) is a 10 frame input window; this includes the frame of the Art Lock (frame 46) plus 9 frames before that. A rB is then successfully performed on frame 47 if the most recent horizontal stick-input during the 10 frame rB input window (frames 37-46) was opposite to Shulk's initial facing direction.
In the most extreme case, a Monado Art Run Cancel (Marc) rB input is inherently limited to 1 frame coinciding with the Art Lock since Shulk must hold forward while running up until the Art Lock occurs. Such 1 frame inputs are not impossible but not consistent, and yet may be aided by ancillary input options like Bidou. Because of this, Marc b-reverse is often the much more realistic movement option over Marc wavebounce.
In a more forgiving example, in mid-air you simple cannot start holding forward again to maintain Shulk's airspeed following your final mid-air rB input during the 10-frame window until after the rB actually takes place on frame 47. This often results in an nominal air speed reduction as Shulk both briefly holds backwards against his current aerial momentum and experiences air friction while not holding any direction--that is, unless the rB can be input the same frame as Art Lock, which is identical to the Marc rB example above.
When utilized in mid-air, a Shulk facing forwards can perform a rB to access Bair's longer threatzone for Fair's better frame advantage. Similarly during a reverse-aerial-rush (RAR), a Shulk facing backwards can perform a rB to access Fair's better frame advantage for Bair's longer threatzone, or reverse-Nair's frame 13 backwards-facing hitbox for Fair's frame 15-17 forward-facing hitbox, or even to land with Dtilt or Standing-Grab facing towards the opponent, thereby eliminating the need to first perform standing pivot.
Doing a b-reverse (Br) means influencing the special move's startup in order to flip both a character's current facing direction and momentum.
The window to input Br (which again is accomplished with a stick-input opposite to Shulk's current facing direction) is a 3 frame input window, starting the same frame a turnaround takes place on frame 47 and lasting until frame 49; A Br is then successfully performed on frame 50 if the most recent horizontal stick-input during the 3 frame Br input window (frames 47-49) was opposite to Shulk's "current" facing direction ("current" means taking into account a possible rB than may have transpired just beforehand on frame 47).
As the abbreviation implies (rB + Br = rBr), doing a wavebounce (rBr) means influencing the special move's startup in order to perform both a turnaround (rB, 10 frame input window from 37-46, performed frame 47) followed immediately by a b-reverse (Br, 3 frame input window from 47-49, performed frame 50). This allows Shulk to only switch the direction of his momentum while retaining his initial facing direction (since flipping his facing direction twice in a row is like not flipping it at all).
Br & rBr via diagonals
You can exploit the fact that the upper two diagonals (unless you use Tap-stick) can count as horizontal inputs to make the b-reverse or wavebounce inputs quicker than normal (versus travelling all the way from left to right or right to left). Combining this principle with the fact that the lower two diagonals both also double as horizontal and down inputs, you can also reflect this motion to reliably input FF just prior to the rBr inputs (the bottom diagonals are indifferent to Tap-stick).
This is a direct consequence of the delayed nature of Shulk's neutral special startup since you don't need to keep the control stick in the neutral position between the rB and Br inputs like you would with any other character's neutral special--those characters risk inputting up or down special instead of neutral special, but not Shulk!
Br & rBr Applications
As with all characters, Br / rBr is most useful as a movement mixup for Shulk, particularly when trying to land. Typically an opponent can read your current aerial momentum and will attempt to punish your landing at the place where your character should land. However, most characters cannot cover a large area of landing easily, so suddenly shifting this momentum in the opposite direction can place you out of the way of your opponent's attempted punish. For this application, either a Br or rBr will work equally well.
The other most relevant application of (FF) Br / rBr is as an offensive tool. This could include full-momentum retreating/advancing aerials for safe/surprise spacing, crossing up opponents, or intercepting low recoveries (i.e. to stage spike or to scoop with AS).
Methods for Easier Inputs
While it is likely that you will develop an internal timer for Monado Art activations simply over time with playing Shulk, there are a few methods for leaving less "guess work" in the timing for your input. Using moves with low FAF, such as jab 1, spotdodge, or roll, you leave only 14-20 frames before the art activates and your window of opportunity for inputting rB / rBr. If you input a jump immediately after the animation is done, your art will activate shortly after you jump (close to the peak of your SH height). This narrower window can be far easier to keep in mind than the 46 frames of a raw art cycle with no actions performed prior.
Using Jab 1 (FAF = 26)
Using Spotdodge (FAF = 27)
Using Roll (FAF = 32)