Suicide Squad: Kill the Justice League

This one is acquired by leveling your squad skills that unlocks once you reach 30 with any of your characters.

Once unlocked you have to level up this new squad skill tree to 50 to unlock the achievement. A side note, the tree won't receive any xp if you switch to another character that is not 30 yet.

Tips to speed it up is to aquire or reroll stats on your weapon and gear so they have xp bonuses. Also put skill points into the xp bonuses found in the squad skill tree.

I had a total of: 44% on kills and 63% on general xp gains to speed my progress up

You should be finding items with experience gain on them and you should be using those at all times. When you have cleared the story and have moved into the postgame, try to hold on to items with Master in the title (the word will also be in blue text). These are better than their other counterparts by a long shot and you should be using these as your endgame build. You should also focus on leveling in a certain way, detailed below too.

Master Items:
1. When you have a Master item, take it to The Penguin to reroll its buffs until it has three. If it already has three, ignore this step.
2. Take the item to Toyman and have him Elite the item, which allows you to reroll all three buffs. This will likely require currency from incursions.
3. Have Toyman reroll the stats (press ) to specify a certain buff for a higher cost. You want to prioritize overall experience gain, not just from kills, since you get experience from completing missions too and that should not be ignored.

Leveling:
1. Each character at Lv30 will give you +3% permanent experience gain. This isn't a lot, but considering you need to get the four base characters to Lv30 anyways, do this before you level up your squad level too much. You could consider reading step 3 below and following that for a few levels between characters since it would apply to any character.
2. Honestly? Get Deathstroke from Season 7. I'm 33hrs in and I'm at Squad Level 14 and Deathstroke was a worthy diversion, at a pretty low time investment. His movement FAR exceeds the four main characters and he's just sick as hell anyway. I have been using only him now - and him being at Lv30 means you'd get another +3% permanent experience boost if you follow in my footsteps. He is the coolest guy in the game and his movement is seriously fantastic.
3. Invest your Squad Levels into experience gain. Yes, this means you sacrifice function from other skills, but you're trying to minimize your grind. With 4-5 characters you can access three experience skills. This would require 60 levels to max out which is unnecessary unless you still have more work to do afterwards, but you'll slowly accrue 0.5%-30.0% more permanent experience gain as long as you keep investing in these skills and nothing else. You should only see this up to +25% since, as said before, you'd need Lv60 to get all the buffs with 4-5 characters.
X. If you're insane and you like this game and want to keep playing it, unlocking all the characters and leveling them to Lv30 would get you a final total of +24% experience and would let you access the five experience skills, which would total to +50% experience, resulting in +74% if you were playing SS:KtJL for way longer than anyone would recommend.

My Advocating for Unlocking Deathstroke / His Movement:
You can do a dash with a string thing in any direction, then jump midair, then do a quick dash in any direction, a midair jump, a second dash, another midair jump, a third midair dash, and another midair jump. Then your meter will be empty. But a dash only costs half your meter and you can repeat the above cycle like four times until it runs out. Your distance coverage is insane and it looks awesome at the same time. You can also do this cool dash thing nonstop on the ground at no cost, whereas Captain Boomerang gets motion sickness if you use the speed force too much in a short span of time. Imagine, if you've played Metal Gear Solid V, the Skull Unit and how they dash around really quick. That's Deathstroke on any surface, and you can hold to do this off rooftops for a little more distance in the air - or jump at the end of a dash to shoot upwards, leading into your first string dash thing.
His moveset involves sniper rifles, shotguns, and assault rifles. If you main him after you unlock him (which you'd want to do since his movement is insane), you can freely disregard most other items - just remember your CPU allies pull from your gear too, so don't leave them hanging!