So there has been some confusion and inconsistencies with the achievement so I figure I'd put what I did here for anybody that's struggling to get this like I was. For starters, lasers refers to the primary weapons and not the beam laser that you can equip to auxiliary.
I did this in a single player AI Fleet Battle. In case you don't know, when you select AI Fleet Battle and the menu pops up you can switch between Co-op and Single player at the top of the menu. I did this on Yavin because of the open space and I played as the New Republic because only hull damage counts towards the achievement and the empire doesn't have normal shielding and default more hull health which equals more damage. I played as an A-wing with the standard lasers so I could catch up to the AI ships easier and also because it's super easy to commit suicide when you need the morale meter to get that extra push against you and prolong the game. This achievement popped for me mid game and I had about 25 player kills and 30 ai kills. What makes this hard is in my experience the AI was pretty good at completing the objectives without me because of the Raider you get when the morale shifts. Time is the biggest factor. I did try to do Ranked Fleet battles but try as I might I couldn't get beyond the 45k mark no matter how much damage I did to players and AI however it may be better if you find the AI fleet battles just keep ending too quickly, bombers in Ranked tend to add the extra hull health to their which makes them a juicy 4000hp target. It's a combination of luck and skill, the luck being that the teams are even enough that the game lasts long and you can get the achievement with some good back and forth
I read on reddit that if you select Nadiri Dockyards, the AI for some reason just gets stuck on the map and you can just kill AI ships and the "players" that are stationary because of the bug. However when I tried it, like 5 times in a row all of the ships on my side and the enemy side just sat back and I couldn't even progress the game. Feel free to try it, I'm sure it'll work for some but I couldn't get it to work.
I've also seen where people said the rotary cannon on the bomber is the way to go too. That's mostly what I did in Ranked Fleet battles and is viable as well, just `not ultimately what I used. It does great damage output if your aim is good.
Finally there seems to be some debate on whether or not dealing damage to capital ships contributes. Based on the wording of the achievement I assume it does and the damage calculator is weird because I had one game with 100k damage to capital ships with only lasers and it didn't pop. The game I got it to pop I didn't do any damage to capital ships and strictly focused on "starfighter damage". Take that for what it's worth as I can't really confirm or deny that it counts towards it but I lean towards it doesn't. If someone can confirm otherwise please do so.