Mass Effect: Andromeda

I'm putting this here because the other solution is a little bit misleading. To get assist medals in a game, you don't need to place 3rd or above in the match, you only need to get a certain amount of assist points. For bronze you need 250 assist points, silver is 500 and gold is 1000. This comes straight from the guide book.

Now, to get assist points, do NOT simply shoot enemies and let your teammates kill them. This gives you DAMAGE points, not ASSIST points. The easiest and fastest way I've found to get assist points is to use the Human Sentinel. Upgrade that push ability and start pushing people around. Any time you use push on an enemy, it doesn't matter how they die, you can kill them yourself, and you'll still ASSIST points. The further you upgrade it, and the more damage it does, the more points you get. It should also be noted that in order for it to work, you need to take down an enemies shields, and it does not work on armored enemies. Larger enemies also grant more points. If you're playing against Kett, the ascendant s can grant up to 250 assist points a pop if you push them every time their orb is destroyed. That's an automatic bronze right there! I'm currently at 20 assist medals so I'll have this shortly myself. Happy hunting!

NOTE: Bandannaboy mentioned a helpful tip that I forgot to put in. If you get a silver or gold assist medal in a game, that counts as 2 and 3 medals, so if you were to get gold medals in all of your games, you could have it done in as quick as 9 nine games.

**Updated**

You have two ways you can earn this achievement; there is no combined count factor here. I'll review both ways you can earn the achievement.

Option 1: Recruit 6 strike teams. This is easily the more time consuming option of the two; however it doesn't take much effort. In the multiplayer menu, visit "Strike Teams". Here you can recruit a team that you can send out on missions and upon success, they'll earn campaign items for your Pathfinder.
It is recommended that you download the "Apex HQ" application on your smart phone. It is a free app that you can link to your Xbox account. From here you can send your Strike Teams on missions from anywhere. Missions take real time to complete.

Your first strike team is "free"; so 5 to go. You'll need 40 "Mission Funds" to recruit your second team. You can earn "Mission Funds" by either completing Apex missions yourself, or by your Strike Team successfully completing missions.
After that, the amount of Mission funds required to recruit a new strike team increases by 40. In the end, you'll need a total of 600 Mission Funds to recruit 6 teams. The amount needed by team is as follows: 0, 40, 80, 120, 160, 200.

If you're in no rush and don't want to play the multiplayer at all, keep recruiting teams and sending those teams out on missions. They'll earn Mission Funds for each successful mission they complete. You'll earn more Mission Funds depending on the difficulty of the strike.
It is recommended that when you're ready to recruit your 6th team for the achievement; that you do it in game and not via the app.

**Update** It has been suggested by a few gamers that you may have to delete the original team you start with; and then recruit your 6th team to unlock the achievement. I did not run into this issue, but for those having trouble it is worth a try.

Option 2: Earn 25 assist medals in multiplayer. This is probably quickest option; but it will require some effort. You earn assist medals based on "assist points (AP)" earned in the match. 250 AP is a bronze medal, 500 AP for silver and 1000 AP for a gold medal. I personally used an Adept and got assist points like crazy.
Also, each medal is worth more points towards your total of 25. A bronze medal is worth 1, silver is worth 2 and a gold medal is worth 3 assist medals. Once you earn 25 medals, of Bronze or higher, you'll unlock the achievement. You can do this in as little as 9 matches if you earn all gold medals.

The easiest way to get Assist medals by far is to play as a Human Adept, which is unlocked from the start. This class has 2 abilities - Pull and Singularity - which can be used to quickly rack up assist points. You get assist points every time you use either of these abilities on an enemy before killing it. If you use both Pull and Singularity, the assist points will stack.

I played on bronze maps and I found it easy to get gold assist medals by spamming Pull and Singularity. I was getting gold medals well before getting to wave 7. Getting gold counts as 3 separate medals, so you only need to get gold in a maximum of 9 matches. I have the PS4 version of the game, but the method is exactly the same for the Xbox One version.

This is by far the quickest/easiest method for unlocking this achievement. It didn't unlock for me after I had acquired 6 Strike Teams on two occasions. I decided to attempt to get the achievement via multiplayer and it popped when it was supposed to.

With this method I was able to get Gold Assist Medals in around 5-7 minutes. I did this by playing private matches on Bronze difficulty. I had the enemy type set as Outlaw. Also, I chose to do it on the map called Firebase Zero but you can do it on any map.

Select the character Human Adept, you need the pull and singularity abilities.

Now, find yourself a position with good cover and let the enemies come to you. Use Pull or Singularity and kill each enemy as they are affected by the ability/when they are floating. This will give you points towards assist medals. Keep doing this for every enemy and you will get a gold medal in around 7 minutes, I was able to get it in just over 5 minutes once or twice. As soon as you see the gold medal appear, let yourself die as it still counts!

Gold assist medals count as 3 assist medals so to get 25 you'll have to play 9 matches or 8 matches with a gold medal and 1 with a bronze.

Doing this I was able to get the achievement in less than an hour!

Attempting this achievement via the Strike Team method is a waste of time. It takes days or even weeks and likely won't even unlock. Don't bother, just do this instead.

Hope that helps!