Shellshifting
Shellshifting is a term that refers to Squirtle's unique dash pivot, and by proxy its advanced uses, in Super Smash Bros Brawl. It gives Squirtle's ground movement significantly enhanced possibilities, much like a wavedash in Melee. There are many applications to shellshifting that greatly improve both Squirtle's offensive and defensive capabilities.
How to Shellshift
Shellshifting is simply a reference to Squirtle's dash pivot animation. When Squirtle turns in the middle of a dash, he will retreat into his shell, slide a very small distance in his initial direction, and then very quickly slide back in the new direction over a noticeable distance before exiting his shell and resuming his normal dash. The physics behind the slide at all stages while Squirtle is in his shell are what make shellshifting very useful in combat. Alternatively, players can cancel the return slide by smashing the control stick back to the original, pre-pivot direction just as Squirtle begins to turn, which will stall Squirtle in his shell without him sliding much at all (though he will still be facing in the new direction when he exits his shell).
Applications
Standard Attacks and Aerials
Squirtle can easily perform all his standing and jumping attacks out of a shellshift, increasing their speed and range (primarily in the eyes of the opponent, who may have previously been chasing the fleeing Squirtle). The jab, forward-tilt, and up-tilt attacks in particular are useful at interrupting the opponent should they be approaching, while short-hopped aerials like forward-air and neutral-airs provide explosive power options for Squirtle, allowing him to once again face his foe in the air as opposed to fighting on the ground.
Squirtle can also perform his Smash Attacks out of a regular shellshift, but all three of them are much better suited for use with slightly different techniques (see Pump Slide below, dash pivot cancel).
Shellshift Dancing
Shellshift dancing is simply the act of perfectly chaining Squirtle's dash pivots together, performing each one as soon as the prior one has finished its animation. This gives Squirtle the appearance of sliding back and forth in his shell while barely exiting. This technique is useful at long-range for confusing one's foe, potentially inducing them to give away or whiff their next move, giving Squirtle the opportunity to capitalize on a possible weakness in the approach. Unfortunately, it is inferior to a proper dash dance, which has a much lower range of vulnerability and can be more easily canceled into an attack (the downside of true dash dancing is that it is far more difficult to perform). Another drawback is Brawl's tripping mechanic, which factors in with each pivot and increases Squirtle's risk of tripping mid-match, making even a regular dash dance less useful than it was in Melee.
Shellshift to Grab
Squirtle's grab range is average on its own, but combined with a good shellshift, he can surprise opponents by returning with a high-speed, mobile standing grab, increasing the grab's range and decreasing its predictability. It is superior to his running grab due to decreased lag and increased distance, and upon grabbing Squirtle often slides a small distance while holding his opponent, making a down-throw KO at high percents even more likely should Squirtle slide his victim to the end of the ledge.
Pump Slide
The Pump Slide is the greatest application of the shellshift technique and is somewhat difficult to pull off perfectly. It allows Squirtle to slide across a tremendous distance (almost all of Final Destination) and do his Up Smash attack. To initiate a SSPS, first do a complete SS (the longest possible slide you can get) and then perform a jump-canceled Up Smash. If done incorrectly Squirtle will just slide a small distance and do his up smash (a regular dashing Up-Smash, or "Hyphen Smash"). It is easiest to do when Tap Jump is turned "on," as the game will register a canceled jump automatically upon performing the up-smash command. However, it can also be done by pressing the jump button at almost the exact same moment as A (the C-stick should not be used). Although the jump technically registers before the Up Smash, it should feel as though the player is pressing the buttons at the same time.
If performed correctly, there are a few ways the maneuver can be put to use. One way is to leave the smash uncharged, which will release the move at roughly the middle of Final Destination while Squirtle himself slides the rest of the distance, making for a very quick mid-to-long range kill move. Another way is to charge the Smash so that Squirtle takes it with him to the end of the stage, releasing a more powerful eruption of water over a longer distance. Either of these methods can be used to simply give Squirtle some defense as he attempts to cross the stage more quickly than either his dash or his Withdraw move would allow.