Here are some points from Arcadia's basic rundown of the Battle Fantasia cast. Listed below is only a sampling of special moves -- please take a look at the file that I recently posted on GameFaqs for a more complete list.
With a standard complement of fireball, anti-air and charging attacks, Urs is easy to pick up and play. His normal attacks have good range and are likewise easy to grasp. Far standing C, in particular, is good for poking and catching your opponent as they try to jump. It can be cancelled, too.
Barify Shot: ↓↘→ + A or C
Projectile attack. The A version doesn't have much range, but Urs has the initiative when his opponent blocks it.
Barify Blade: →↓↘ + A or C
Shoryuken! How difficult will it be to use Gachi Match against this multi-hit anti-air move?
Ba-ku-o-n Roadmaster: ↓↘→↓↘→ + A or C
Urs quickly rushes towards his opponent a fair distance. Good for combos and counter attacks.
Certain special moves get powered up. Some become able to knock Urs's opponent off their feet, others do extra hits, etc. Zero Yon Glide becomes a big combo tool. Use it after an upper Gachi Drive and then continue to juggle with the powered-up Barify Blade.
Marco also has some standard Shotokan-style fireball and dragon punch special moves. His floaty jump means that air combat isn't his speciality but he has a quick dash and a good up-close game. Hit confirm rapid fire crouching B into a Jigoku Slash. Poke with towards + C at medium range.
Dokuhebi Crush: ↓↙← + B or D
Leaping overhead attack. Hold the button down and Marco will hop forward without attacking.
Final Strike: ↓↘→↓↘→ + B or D
Marco holds his sword up and blasts his opponent. Good invincibility for anti-air and interrupting your opponent's attacks.
Marco summons the dragon Charshu. Make your opponent block the multi-hit Charshu Fire attack and look for a high-low mix-up.
Using a flag as a weapon, Olivia's various C attacks have excellent range. Her jump attacks are particularly dangerous. Mix these up with the Empress Lily special move to throw off your opponent's anti-air Gachi Match timing. D attacks leave flowers behind.
Dainty Libby: ↓↘→ + A or C
This charging attack has some recovery time so it's useful mostly for combos. Cancel her crouching C into a Dainty Libby for a good mid-range combo.
Shall we dance? →↘↓↙← + A or C
This command throw inflicts only one hit point of damage, but it's possible to land a follow-up attack.
Olivia summons four doves that peck in conjunction with her attacks. These extra hits go with all of her moves, from normals to supers. Break your opponent's defense with the towards + B overhead and then proceed to combo into Dainty Libby -> Centifolia for big damage.
Closing in on his opponent with quick jumps and rushing special moves and then using an attack/command throw mix-up is Ashley's game. Jumping D has excellent priority down and to the front and jumping B stays out for a long time. Do down + C in the air and Ashley will float for a moment; use this to disrupt Gachi Match attempts.
Glance Wing: ↓↘→ + A or C
Ashley flies straight ahead. This move has a sizable recovery so save it for hit confirming and counter attacks.
Judas Wing: →↓↘ + B or D
Ashley leaps up and attacks his opponent at a downward angle. As long as you aim for your opponent's legs you should be pretty safe when it's blocked.
Steal You: →↘↓↙← + A or C
Command throw with decent range.
Activate Heat Up! and Ashley gains access to the Romance Wing special moves. These look similar to his Glance Wing but differ in that he can cancel one charging attack into a different one. It's possible to combo your opponent all over the screen. One way to set this up is to connect with an upper Gachi Drive, start Heat Up! and then immediately juggle with a Romance Wing.
A classic charge character, Cedric can use his fireball to keep his opponent at a distance, or he can throw one and then approach behind it. It's possible to get closer to your opponent while maintaining a charge by using back + B. In a similar fashion as Third Strike's Remy, Cedric can launch with crouching C and then juggle with a Holy Devotion (Flash Kick) attack.
Evangelical: ← hold, → + A or C
Sonic Boom! Projectile attack with very short recovery.
St. Drop Kick: hold D, then release
Kick gets stronger the longer you hold the button down.
Hammer of the Gods: ↓↘→↓↘→ + B or D
After starting this move, if Cedric's opponent attacks he'll trap them in a giant bell and hit it repeatedly.
Cedric powers up his special moves. Most importantly, his Evangelical attack throws two projectiles that travel at different speeds. Chase in behind them and use a towards + D overhead or some other mix-up variation.