Robin would wield a Silver Sword as his main weapon, with an unmarked tome strapped to the inside of his coat that he'd take out to cast a variety of spells (and as kind of an aesthetic cheat, so he wouldn't be pulling a bunch of different tomes out of hammer space). His playstyle would emphasize having options at any time, allowing him to control the battlefield and the flow of the fight itself, and would both encourage and reward being one step ahead of opponents. I refer to Robin with male pronouns here for consistency--the female version of Robin would obviously have the exact same move.
(This is a variant-based moveset--the alternate specials are based on the default ones. A lot of relative terms are used because I've been out of practice and I don't want to accidentally make a move too strong or weak. And special thanks to Hong/Esmoire for inspiration for the Neutral and Down Specials.)
Neutral Special (1): Elfire
Robin wields his tome in one arm, extends the other arm forward, and a cluster of flame materializes in front of it. The spell's size is modest--not huge, but big enough. (You know that pic comparing two sizes of Lucario's Aura Sphere? It's a little bigger than the small one.) As soon as the spell appears, Robin pushes it forward with the speed of Din's Fire...but after half a second, it starts slowing down drastically, and by the time another full second has passed, it'll have stopped completely and will hang in the air for another 2-2.5 seconds before dissipating. If B is held at the beginning, Robin can use the left stick to guide the spell's trajectory--it isn't full control; more like nudging it in the direction pressed, but enough where an experienced Robin will be able to make it go more or less where he wants. When the player lets go of B, the spell continues on its current path, and Robin can create another one. Up to three Elfires can be on the field at a time; if three are in play when the player presses B, Robin performs the starting animation but nothing appears. Damage and knockback are mid-low, with a fire effect.
Elfire is best used to trap opponents and provoke them into moving where you want...but the damage is enough to be worth landing a hit.
Neutral Special (2): Elthunder
Instead of fire, Robin summons a ball of lightning. This version deals a little more damage and knockback than Elfire (and an electric effect, of course), but to compensate, it's more difficult to guide.
Neutral Special (3): Nosferatu
Plenty of canon movesets take some creative liberties, and hey, Robin
can wield dark tomes if he changes to the proper class. This version summons an orb of swirling darkness that deals, naturally, dark-elemental damage. Unlike the other two versions, only two can be on the field at a time. The charges are smaller and as hard to control as Elthunder...but deal slightly more damage than Elthunder, and even heal Robin for half the damage dealt! Knockback starts out greater than the other two--to make them harder to chain hits between--but scales more slowly, becoming closer to Elfire's knockback at higher percents.
Side Special (1): Thoron
Robin spins once in place, shouts, and extends his arm forward. A crackling ray of lightning fires out from his palm across the arena, and very quickly reaches a distance 1 1/2 times the length of Battlefield with a height equal to half of Ganondorf's Brawl height. Thoron charges over time, similar to R.O.B.'s Robo Beam; if used in quick succession it decays to as little as half its height and 1/6 its full distance. Damage and knockback are moderate at full charge, scaling back the lower the charge.
Thoron can kill in a pinch, but its main use is as a long distance poke and a way to threaten opponents from a distance and force them to move somewhere more favorable to you or dodge/shield and give you a chance to capitalize. Much stronger than Robo Beam, but ideally it'd be balanced out by being more telegraphed. It also, of course, has an electric effect when it hits.
Side Special (2): Arcfire
Robin shoots a stream of fire from his hand. Deals less damage than Thoron, but recharges a little faster, has a slightly taller hitbox, and has a fire effect.
Side Special (3): Forseti
Completing the trio is...the other Anima element. Robin fires off a cylinder of violently swirling, blue-green air. Takes a little longer to recharge than Thoron and travels notably slower than the other two versions...but has the height of Arcfire, the damage of Thoron, and enough additional knockback to be a viable edgeguarding tool!
Up Special (1): Rexcalibur
Robin raises his arms to his sides, summoning a vortex of spinning blue-green air around him that rises upward and carries him with it. Anyone caught in the wind takes multiple small hits--think Mach Tornado sans pulling the enemy in. Rises at moderate speed--about what Squirtle's Up-B did in Brawl--and lasts long enough to give Robin distance 1 1/3 the height of Marth's Dolphin Slash. Robin can move himself and the vortex left and right to an extent. When the move ends, Robin cannot use other special moves until he touches the ground, but he can use regular aerials and dodges.
Robin's recovery move lets him cover some distance while giving him some breathing room to do so. The attack has low-ish priority, though, so non-physical projectiles or a well timed disjointed hit will knock him out of it. Plan accordingly!
Up Special (2): Wilderwind
Rexcalibur with an offensive-minded twist. The vortex is lime green in color, and smaller, making Robin that much easier to knock out of the attack. However, its hitboxes chain together more easily, and it finishes with a powerful final hit!
Up Special (3): Celica's Gale
Want to have more control when you need it most? A rose-tinted vortex surrounds Robin that gives out half as early as Rexcalibur...but then a
second one forms around him, allowing him to re-angle his trajectory or even increase his momentum in the direction he's already moving in! There's a cost, though; it doesn't rise as quickly and therefore only gets Robin about 3/4 of Rexcalibur's vertical distance.
Down Special (1): Ignis
Robin stands in place, opens his tome, and focuses as the B button is held. Over the span of two seconds, he begins to glow azure blue. When fully charged, he slams the tome shut and a sound rings out...you know, like the one when a critical hit or a skill activates. The next attack Robin lands will deal 1.5x its normal damage and have increased knockback!
...And the obligatory cloud of flower petals, of course.
Not every Fire Emblem character needs a Down-B counter. Ignis gives Robin a way to prepare for his next attack during a break in the action. If you've sent your opponent flying, will you follow them to finish the job, or focus to ensure your next attack is the killing blow?
Down Special (2): Solidarity
Robin begins to focus, but this time he glows a brilliant gold (actual gold, not yellow). Once charged, Robin gains minor knockback resistance for the next 10 seconds, and his attacks deal slightly
more knockback themselves!
Down Special (3): Lifetaker
Robin focuses again, this time glowing a sickly shade of green. Once charged, the next attack he lands will heal him for half the damage dealt! If it's a Nosferatu spell, it heals him for
all the damage dealt!
(Yes, I know this functions closer to Sol, but Lifetaker felt better thematically. That, and it comes from another sword+tome class. >_>)
Final Smash: Rally Spectrum
As he channels the limitless power of a Smash Ball, the screen focuses on Robin and freezes in place. Robin gestures and shouts one of his
critical hit lines, and an aura surrounds him that shines in every color imaginable. For 20 seconds, Robin gains moderate boosts to movement speed, damage, knockback, and weight (that is, launch resistance, not fall speed).
Sound underpowered? But in team battles, any of Robin's allies
also receive the same boosts!
(And, if you trigger it when the crowd is chanting Robin's name, they'll shout the crit line with him! We've all done that before, haven't we?)