For most people, including myself, your kill counter will reset if you swap games. Like, if you have 999 kills in ME1 and you click on ME2, you can very likely lose all progress toward this achievement
My personal favorite method for this achievement is one you can do very right after you gain control of the Normandy in Mass Effect 1.
It involves the mission UNC: Lost Module with the monkeys you can use to glitch infinite paragon points. This mission is located in the Attican Beta system - Hercules cluster - planet Eletania.
Look at the map and go to the orange marker that is on the right side of the map. You will start the mission here.
The correct area out of the three monkey colonies that are highlighted on your map is the middle one. It has a structure next to it (you need to go in here to finish the mission).
Drive up the structure and park in between the monkey nests. Save your game.
Use the Mako to kill all monkeys, reload, and repeat.
I was killing 10 monkeys about every 10 seconds. Starting from 0 kills (because of a glitch), I reached 2000 kills in about 30 minutes. (And this achievement in about 15 obviously)