A bit more in depth:
Note - if you previously met this score requirement prior to the update, it will automatically unlock upon playing the game. No need to get it again.
You are required to end with a score of 400,000. This challenge is a green icon on your map to the right of the Crown Blades Factory fast travel.
For me, this was definitely the hardest of the 3 achievements in this DLC. As with the "I should get paid for this" achievement, I would not recommend attempting this until later in the game when your weapons are upgraded and you have access to more amps/overdrives.
Start with your overdrive setup:
• OD Rival
• Weapon Damage – Deployables
• Weapon Damage – Single-shot
• Ammo Capacity - Deployables
• Ammo Capacity – Single-shot
• OD Killer
For weapons, I would choose from the following:
• Acid Sprinkler
• TNTeddy (Nuke Explosions)
• Pulse Mine or Proximity Mine
• Hairspray Bomb
IMPORTANT - USE THE SECOND AMENDMENT AMP ON YOUR MAIN WEAPON AND AMMO WILL NOT BE AN ISSUE
Unlike the other score achievements, spamming your weapons alone won't get you the score you desire. You must complete the challenges Buck requests of you to get your score up quick enough. The challenges are straight forward, repeating, and are in order as follows: Bounce Kills, Grind Kills, Blower OD Kills, Pain Train Kills
Bounce kills and grind kills are self explanatory. When the blowers appear, already be shooting your weapons at the top of the two water towers. I found that they rarely had time to jump down and had my kills within a few seconds.
When the pain train challenge comes up, be sure not to kill the OD you paralyze on the track. They swarm ONCE specifically for you to hit the switch, but if you kill them off in a blast of hairspray, you'll be hard pressed to get them grouped back together again and will require multiple switch hits (thereby killing your score).
Personally, I used the hairspray bomb for the duration of this challenge. This overdrive setup covers use of deployables but I preferred not to use them considering the Pain Train kills Buck wants from you. They can certainly be effective if deployed away from the railroad tracks and can do much of the challenge-completing for you.
Please be sure to vote and comment if you give me a negative so I can improve this guide! :)
edit: video you can use as an example -