Kill enough enemies using Barricade to cross the points threshold and this challenge will be completed. Any difficulty, enemy, or map will count towards this challenge.
The challenge description does not explain how to get points for this challenge. Barricade will have to be upgraded to high ranks to unlock specific abilities to earn points.
There are several methods to get points:
Upgrade to Rank 5A Weapon Feedback or 5B Power Feedback — When a barricade is deployed, +20 Support will show on screen. Each time a new barricade is deployed this will happen. This is a very slow and laborious process to earn points.
Upgrade to Rank 6B Electric Defense — Points will be awarded each time an enemy is damaged and/or killed by the electric shock of the barricade. Enemies will have to run up to and be hit by the barricade to show visible electric arcs over their body for the points to count towards the challenge. This method is faster for earning points towards the challenge but requires enemies to be close enough to cause harm.