Challenges replace full synch requirements in Assassin's Creed Unity.
Challenges are only on the story missions and provide a couple extra optional objectives to complete during a mission.
If you fail to accomplish a challenge your first time around, you can replay a story mission by going to your progress tracker, selecting the memory, and pressing A to replay it.
Also, if you fail a challenge during a mission, you can retry at a checkpoint in order to not have to complete the entire mission again.
For the assassination missions (black boxes) I recommend completing the mod missions as these usually make the challenges easier to complete.
Here are the challenges for all the missions that require them:
1-1: Pass over/under objects (5)
Don't get tackled
1-2: Parry Attacks (2)
Dodge Attacks (2)
1-3: Don't get into conflict
2-1: Perfect Parries (3)
Smoke bomb evasions (2)
3-1: Cover kills (3)
Keep up with Bellec
3-2: Hiding spot kills (2)
Don't trigger any alarms
4-1: Cherry Bomb Lures (2)
Phantom Blade Kills (2)
4-2: Air Assassinations (3)
Phantom Blade kills (2)
5-1: Brutes driven beserk (2)
Doors lockpicked (4)
5-2: Pistol Kills (3)
Pass over/under objects (4)
5-3: Alarm bells sabotaged (4)
cover kills (3)
6-1: Beserk Snipers (2)
Hiding spot kills (2)
6-2: Headshots (4)
Double assassinations (2)
7-1: Enemies stunned (3)
Headshots (3)
7-2: Pass over/under objects (5)
Use a lift
7-3: Don't get knocked down
Staggering strikes (5)
8-1: Cover Kills (3)
Alarm bells sabotaged (3)
8-2: Cover Kills (3)
Ledge assassinations (3)
9-1: Don't touch the water
Don't trigger any alarm bells
9-2: Rescue Thomas Levesque
Don't trigger any alarm bells
9-3: Don't touch the ground
Keep up with the Montgolfiere
10-1: Double Assassinations (2)
Beserk Brutes (2)
10-2: Kill Snipers (2)
Stun Guards (5)
11-1: Cherry bomb lures (4)
Poison Bomb Kills (2)
11-2: Headshots(3)
Cover Kills(4)
12-1: Sabotage Alarm Bells (1)
Don't let Elise get detected
12-2: Don't get into conflict
Lockpick doors (1)
12-3: Double Air Assassinations(3)
Sabotage Alarm Bells (2)
Below I have included my video series on ACU's challenges.