General playstyle description and justification:
Edelgard uses her signature axe, Aymr, in Smash Bros. She's the shortest of the current Fire Emblem cast, but not by a large margin. She's not very quick, about on par with Mii Swordfighter, while also being decently heavy due to her axe.
To offset these characteristics, her playstyle revolves around taking full control of and limiting the opponent's movement options, allowing her to more easily get a few solid hits in. In Fire Emblem Three Houses, one major new feature is the Battalion and Gambit system, which works off of the user's Charm stat and Authority level. By selecting a Gambit, a battalion of soldiers joins a unit for a group attack, and these can have various effects.
One common theme is limiting the target's options. Opponents can't counter attack, Gambits often leave Beast units dazed and unable to strike, and when used on normal enemies, they often prevent them from moving at all.
Edelgard's best combat ranks in Three Houses are Axes and Authority, which would make up her moveset here. This also showcases her personality, as someone who always has a plan and leaves nothing to chance. By eliminating the opponent's escape options, she forces them to face her head on, where she can then deliver a decisive blow.
Jab - A two-hit combo attack, wherein Edelgard hits the opponent in a chopping motion with her axe, alternating which side she swings from.
Dash Attack - While running, Edelgard swings her axe upward from the ground in an arching sweep.
Forward Tilt - A two-strike attack, similar to Meta Knight and Piranha Plant. On the first hit, Edelgard sweeps her axe from the side, and the second hit has her continuing the motion as she swings it downward from overhead.
Up Tilt - Edelgard swings her axe from the ground to above her head in an almost golf club-like motion.
Down Tilt - While crouching, Edelgard kicks outward while holding her axe close by.
Neutral Air - Edelgard swings Aymr in a complete circle around her body. If this move is held, she keeps performing this move and each subsequent swing gets a lightning effect with high hitstun.
Up Air - Edelgard performs a motion similar to Ike's old up air, but with a fire effect imbuing the axe.
Forward Air - Edelgard slams Aymr downward in front of her, and if the foe makes contact with the spiked end, they get, well, spiked.
Back Air - Edelgard swings Aymr behind her. If an opponent is hit, a small explosion-like fire effect activates and launches them backwards.
Down Air - Edelgard slams Aymr downward, falling downward with it. If she hits an opponent in the air with it, they both plummet straight down and, upon hitting the ground, the foe takes very high damage. The move has a lightning effect to reference the Lightning Axe art.
Forward Smash - Taken from her own Smash combat art, Edelgard leaps forward and smashes Aymr into the ground in front of her.
Up Smash - Edelgard thrusts Aymr skyward as a giant projection of the Crest of Seiros envelops it, the sigil doing rapid multi-hit damage before exploding.
Down Smash - Edelgard ducks down and spins Aymr along the ground in a circle as one fluid motion. Shortly afterwards, the circled area around her bursts into flames for an additional attack.
Pummel - Edelgard grabs the foe and bashes them with Aymr.
Forward Throw - Based on the Smite maneuver, Edelgard launches the foe forward with high knockback by swinging her axe at them. This is a powerful kill throw.
Back Throw - Edelgard throws the opponent, slamming them into the ground behind her.
Up Throw - Edelgard uses one hand to launch the foe skyward.
Down Throw - Edelgard throws the foe into the ground beneath her.
Neutral Special - Flickering Flower - Edelgard readies her stance as Aymr takes on a red glow. Upon releasing the button, she swings the axe with full force. If an opponent is hit by this move, they won't take much damage, but will receive massive hitstun as a small explosion effect holds them in place for a short while. Edelgard can then follow up with a strong Smash Attack, or regain space by leaving the foe there.
Side Special - Hand Axe - A simple projectile and one of Edelgard's faster attacks. Edelgard takes a small throwing axe and tosses it. It will then spin through the air as it flies, before hitting the ground and disappearing. If foes are hit with the blade, they will take much more damage than if hit with the handle. The blade will also do significant shield damage. While the move is fast, it cannot be spammed easily, as only one Hand Axe can be on the screen at a time per Edelgard.
Up Special - Raging Storm - Edelgard takes from one of her Critical Hit animations and leaps upward with Aymr held high, and then crashes downward at a diagonal. The move has a rising hitbox with Aymr's head, but it can be cancelled before reaching the full height. This, however, loses the hitbox. This attack acts as a mix between Cross Chop and Super Dedede Jump.
Down Special - Fusillade - Edelgard makes an exaggerated wave of her hand and yells "Now!" From the fourth wall, a volley of arrows from an unseen imperial battalion rains down in a column shaped area in front of her, covering the same amount of height as Palutena's up smash. This attack can be used for edge-guarding purposes, as airborne opponent's will be slightly pushed downward for each arrow that hits them. However, if Edelgard is in the air when she uses this move, only one arrow will be launched, reducing the move's effectiveness. This move also has a small cooldown after it's used, so use it wisely.
Final Smash - Raging Flames - Edelgard whacks a nearby foe with Aymr, triggering a cutscene as "Gambit Boost" flashes onto the screen. A cart full of explosives is wheeled toward the knocked down foe. Edelgard is joined by Byleth and Hubert. Edelgard gives the command as Hubert fires a Miasma toward the cart, the latter laughing all the while. The cart explodes on contact with the target as the cutscene ends and the foe is sent flying.