Turbo Golf Racing

I did this by using a console and my phone w cloud gaming, and 2 profiles. But could also be done with a friend/2nd online console.

From the Main Play menu hit to change game mode. Select Custom -> Host Game. I then changed the General setting to Private games, 8 players, any region, Bots (on or off, i had them on when i did this), bot difficulty Easy. You're welcome to select whatever 3 levels you want but I just did random levels. Allow all pickups (so you can work on the pickup achievement) then in Cores de-select any Active Cores (orange/gold border) you've already won with, or just keep track of what you've done.
Once done w that hit hit Host Game, this will put you back and the Main Play screen and you will be in a party of 1, hit and tab over to Friends. Invite your friend/2nd profile. From the 2nd profile accept the game invite through xbox (doesn't ask through game) you will now be in a party of 2 and can play "easy" online games wither easy bots or with just the 3 players, and they count as online games.

Now select a different Core after every win (3 matches) and the cheevo should pop. I got stuck the most on forgetting which Cores I'd already used.
This method can also be used for the 10 passive cores achievement.

Season 3's update has finally fixed this, the other Core achievement and the Dailly Missions achievement.

To unlock both core achievements you just need to win the game with different cores.