Astral Heat - Successfully complete Arcade mode with a character to unlock their Astral Heat. Note: Ragna already starts with his Astral Heat.

Unlimited characters - Successfully complete the indicated task to unlock the corresponding character:

Unlimited Hakumen: Successfully complete Hakumen's Arcade mode.
Unlimited Rachel: Successfully complete Rachel's Arcade mode.
Unlimited Ragna: Successfully complete Ragna's Arcade mode.
Unlimited v-13: Successfully complete v-13's Arcade mode.

Play as Hakumen and Nu - Get a 100% completion with all ten starting characters to unlock Hakumen and Nu.

Fight Unlimited Ragna in Arcade mode - Get a "Distortion Finish" more than ten times and do not lose any rounds. You will be challenged by Unlimited Ragna after your last opponent has been defeated.

Japanese audio interview - Get a 100% completion in a character's Story mode to unlock the bonus audio track in Gallery mode for that character.

Alternate ending - Successfully Story mode with all characters to view the true ending.

Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Dante (30 points): Beat Arcade mode on the highest difficulty.
Leonidas (40 points): Beat Score Attack mode.
I Am the Just Sword (20 points): Defeat Hakumen in Arcade / Score Attack mode.
Murakumo Activated... (20 points): Defeat v-13 in Arcade / Score Attack mode.
Wanderer (10 points): [Player Match mode] Experience a Player Match.
Warrior (30 points): [Player Match mode] Experience is power.
Voyeur (10 points): [Player Match mode] Learn from the mistakes of others.
Ruler of Kagutsuchi (10 points): Fight against different opponents in Ranked Match / Player Match mode.
Be Gentle... It's My First Time. (10 points): Experience a Ranked Match.
That Was Incredible! (10 points): Conquer a Ranked Match.
You Brute! (20 points): Win several Ranked Matches in a row.
100 Trials (20 points): Strive higher in Ranked Matches.
200 Trials (40 points): Strive even higher in Ranked Matches.
Hands Where I Can See Them (30 points): Collect more art in Gallery mode.
I Like to Watch (10 points): Collect replay data in Replay Theater mode.
Hello World ! (10 points): Understand the truth of the story in Story mode.
You're the Best! Around! (20 points): [Training mode] You still have much to learn.
Legionnaire (20 points): Increase your level.
Praetorian Guardsman (30 points): Increase your level even more.

Additionally, there are 31 secret achievements:

Words Hurt Too (30 points): Let an opponent get a 5,000 hit-point lead on you, then taunt you.
Designated Driver (30 points): Used Distortion Drive over 100 times.
Their Numbers Count for Nothing (20 points): Performed an instant block 300 times.
Greased Pig (10 points): Successfully escaped 50 throws.
Restraining Order (20 points): Used Barrier Burst over 30 times.
I'm Faster Than Anybody (20 points): (Ranked/Player Match) Get "First Strike" five times in a row.
Hat-Trick (10 points): In one match, successfully pulled off "Thirteen Orphans", "The Great Wheel", and "All Green".
In Living Color (10 points): Used all the color palettes of a single character.
It's Go Time (10 points): Performed your first Astral Heat.
Devil's Advocate (20 points): Used Ragna's "Gauntlet Hades" over 100 times.
This Is Important... (20 points): Heard Noel say, "Hands off the panda!" over 100 times.
I Can Rebuild Her... (10 points): As Carl, decommissioned Nirvana three times in one round.
Activate Termination Protocol (30 points): Completed a 60+ hit combo using Nu.
Nothing's Gonna Keep You Down (30 points): Earned a Perfect victory 30 times.
It's over 10,000! (30 points): Dealt over 10,000 damage using Hakumen, without the use of an Astral Heat.
Bangarang! (20 points): Fought against Bang as Bang, and both activated the "Fu-Rin-Ka-Zan".
Cat-a-pult (10 points): Threw a Kaka kitten using Taokaka's "Kitty Litter Special!".
It's The Only Way To Be Sure (10 points): Performed a 20 hit combo after the round is over.
Dun Dun DUNNN! (30 points): (Story) Saw the True Ending.
Animation Conservation (20 points): Used Rapid Cancel over 100 times.
Victory Is an Illusion (30 points): (Arcade/Score Attack) Defeated "Unlimited" Rachel.
Beautiful Arakune (20 points): Had a perfect match using Arakune.
Spoonfull of Sugar (20 points): Stayed afloat for over 25 seconds with Rachel.
Carpal Tunnel (20 points): Exceed a total playtime of 25 hours.
Welcome to the Azure Nightmare (30 points): (Arcade/Score Attack) Defeated "Unlimited" Ragna, and obtained the power of darkness.
Stop Hitting Yourself (20 points): Used Counter Assault 30 times.
Ride The Icening (10 points): Used Musou Senshouzan or Tosshougeki over 20 times in one round, and finished the opponent off.
This Just Got Real (20 points): Caused a Double Down to occur.
You Never Forget Your First (10 points): Performed your first Barrier Crush.
Discouraging Finish! (30 points): Use an Astral Finish with every character.
Irresistible (10 points): Hit the opponent with Tager's "Spark Bolt" more than six times in one round.