Battleborn

Cloak and Dagger: Kill 100 enemies with The Element of Surprise. (Used to be 500)
Element of surprise is the short period of bonus damage that triggers after leaving stealth (after decloaking after using her clone ability), denoted by a orange effect on the edge of your screen. Fastest way to grind this is PvE vs swarmers that infinitely spawn in the icy part before the 2nd miniboss of the Alogrithim level. Just don't kill the spawners.

One Step Ahead: Stealth with less than 20% health, 30 times.
Essentially use her clone ability while under 20% health, shields do not matter. Best way to grind this out is to play the first level, get damaged to ~100 HP left then retreat to the spawn and spam the first ability.

War is Hardly Civil: Deal 10,000 damage to Rendain.
Rendain is the last boss of the last level Heliophage. Damage to his shields count and you should probably get this in 1 game, unless you team is good. Can be easily farmed while going for ulti damage since that takes the longest time and there is a dedicated Heliophage playlist if you don't want to go it alone.

Fan of the Empire: Deal 60,000 damage with Blink Storm.
Blink storm is Deande's ultimate ability (Y). Does damage and stuns enemies in a small cone in front of her. To get this just use your ultimate whenever it is off cooldown, prioritising bosses and groups of enemies. Probably the slowest of these challenges but not difficult, should come after ~4 PvE games.

The Seeds of Secret Orders: Play 3 matches on the same team as Ambra.
Grab a friend and get them to play as Ambra, or wait to pick your Battleborn until others have and take Deande if they take Ambra. Alternatively use a second controller and play splitscreen with Ambra - she will need to be unlocked for the second player seperately so this can be annoying.