Sunset Overdrive

For this achievement make sure you have a fully upgraded hairspraybomb with the second amendment amp. Once you start up the challenge Buck strikes back equip the hairspraybomb and go grind on the lines with christmass light now just start killing everyone and don't do any challenges except the very first one. This will easily get you the 500.000 points.

Unlike the "I Should Get Paid for This" and "Hardcore!: Buck National vs The Apocalypse" achievements, where I could only succeed by performing the specific challenges suggested by Buck, for this one I was able to get a lot more points by doing my own thing:

1- Having the following weapons at level 5 and full of ammo:
- Acid Sprinkler, Hair Spray Bomb and Turret Copter;

2- Having the following overdrives equipped:
- Weapon Damage and Ammo Capacity for deployables; Weapon Damage and Ammo Capacity for single shot weapons; Killer of ODs; High Style by bounces (my favorite action to perform);

3-
- As soon as the challenge starts, get high in the air and start spreading your Turrets and Sprinklers around to build up your "combo" meter. Remember that you will have to redeploy them every once in a while, when they expire.
- While those deployable weapons do the work of making sure your combo doesn't stop, keep bouncing and use the Hair Spray Bomb to shoot the farthest enemies. Just keep the chaos going and killing every enemy you see.
- Completing the challenges given by Buck is totally optional and you really shouldn't focus on them.
- You will naturally get more than enough points (in my case, without trying too hard, 633600) just by killing large groups of enemies at once or in a few seconds apart.

If this solution helps you to get this achievement too, please let me know by leaving a thumbs up and a comment if you'd like.

I also equipped the Second Amendment amp, but I didn't have the Hairspray Bomb yet so I'd say just use whatever weapon you have that can kill the quickest, then memorize the order of the challenges (grind kills>melee kills>undergrind kills>bounce kills>blower OD kills>electric barrel kills) so you can already be heading towards the next challenge when you finish one. Completing challenges is the key, here's when I finally pulled it off:

So I was using the other solutions mentioned and having a lot of difficulty breaking 450-490k each time.

My method for this achievement was to use all of the amps mentioned but using the Murderrang level5 with the Second Amendment amp. This made getting kills a complete cakewalk, I could traverse the map and complete objectives and on my first attempt I scored 680k. Might not work for everyone but it made this 100x easier.