Mass Effect 2

A good place to farm this is on the legion loyalty mission on The Phoenix Massing. I used miranda since she had the overload ability for one of my squad mates (it defaults to legion as the other).

You can get your 1st one as you enter the initial area of the base. After that you will have 2 cannons you can hack and use on enemies and one of the enemies coming out the door has a shield. Use your ability on that one after a quick time slowdown and a shot or 2 with a gun. You will then enter a room with 2 more you can do. Slow down time, a few shots to take out part of the shield, use miranda for the overload and then hit the other one towards the door at the other end of the room.

You now have 4 total and then you just reload the autosave and get another 3. Takes maybe 10 minutes to get all 25 done. Get your 3 and keep reloading the autosave until the 25 are done.

The absolute best place to farm this would be right after you speak to Tali on Freedom's Progress. Be sure this is on normal difficulty as Overload with destroy the droids in one hit. Right before you leave save then make your way out Miranda should tell you to Overload the next few enemies there are a total of 12 but they are weak so you can only get a few now fight your way up till you get to the door where you have to fight the giant mech then just reload your save. Doing this a few times will net you the achievement.

I got this achievement on Tali's Loyalty mission with Garrus after you board the ship that was overrun with Geth.

When you go through the first room you're attacked in, there are two laptops and a Quarian log there in the back righthand corner. Take care of those and continue to the left into the hallway. Go right and take the second left after you find the Geth technology in the first room on the left. There is another Quarian log in the hallway. Go ahead and read it. You can save right here, or use the Autosave the game gives you before you open the next door. When you open that door, a Hunter will come into the room. You can use Overload on him there to knock down his shields when he comes down the stairs. Right there, there is another log, and a Wall Safe. Go up the stairs to trigger the Geth. One of them is another Hunter. Back down the stairs and wait for him to come around the corner to come down after you and Overload him. Basically, repeat this process of going up the stairs to make sure they know you're there, then go back down and let your Overload take care of them when they come around the corner. Be careful in "weakening" them before Overloading them - by this time in the game, you weapons may be too powerful. As soon as you see them - just hit them - the Overload should take the shields down even if they're full. If you DO get the shields down without Overload, you can use Tali's AI Hacking to have the Geth regenerate their shields. One bonus to doing this is that the Geth will just stand still right there for about 10 seconds.

Never go into the room at the top of the stairs (I didn't because of fear of an Autosave). You can get a good 5-6 Geth with shields this way. Once you've gotten them all, just reload your save.

It took me maybe 15 minutes to get the achievement here.

The absolute easiest enemies to get this with are the tripod drones. They have only weak shields (on Casual), no health, and always come in groups of at least 4. These shields can be taken out with one use of Overload.

When you encounter them, make sure that your squad power usage is set to "Disabled." This way they cannot use any powers unless you order them to, since you cannot get the achievement unless you specifically ordered them to use Overload. Just save before an encounter with tripod drones (or any shielded enemy) and keep reloading the save until you have it.

The DLC mission "Overlord" had at least 2 groups of drones for you to destroy in Vulcan station, which comes up later in the mission. They are also encountered in the main game, the earliest time being in the second mission "Freedom's Progress". For best results, take two allies with Overload (Miranda and Garrus have it).

If you went an infiltrator this is really easy once you obtain the AI hacking power, Whenever you see a LOKI Mech just use your AI Hacking ability on it to give it a shield, then you can use Garrus or Miranda to use overload on the Mech.

I got this on Tali's loyalty mission. Using Miranda and my own overload power. Ordering Miranda to use over load as often as I could and using it my self whenever I saw geth with a shield. I am fairly confident that AI hacking which Tali has gives the geth a shield which you can later break using overload to help you get this achievement.