Here's a way for multiple players to get Onyx stars from a Declassified Mission while using the split-difficulty/dropping out trick. I've written the guide based on 2 players but it works fine with 3 or 4.
This method can't be used in split-screen. Credit to LeiChat
who confirmed that you can incorporate split screen players but that the split screen players can only drop out together (therefore you can't use this trick in a 2 player split screen game but can include split screen players in a 3 or 4 player game).NOTES BEFORE YOU START
To speed things up I'd suggest everyone get into an invite only XBox Live party so that the person or people quitting out can rejoin the game without the need to send invites. Hopefully it goes without saying that the in-game party should be set to invite only.
1. Load the game from the main menu with player 1 (the host) on Insane and player 2 on Casual and earn the 3 stars. These will show as bronze stars at the top of the screen while earning them as player 2 is on casual.
2. When you get to the part where you have to press up on the D-Pad to finish the Declassified Mission player 2 should quit out.
3. At this point player 1 is in the game on their own with 3 bronze stars showing. Finish the mission by pressing up on the D-Pad and you'll be given 3 Onyx stars instead - YOU NEED TO STAY ON THE STARS SCREEN!!
4. If player 2 joins back in while player 1 is admiring the 3 Onyx stars then player 2 will also get the Onyx stars. Player 1 has to wait for them to see the stars and then continue onto the next section for them to count for everyone in the game.Please Note
Just to let you guys know, player 2 (and 3/4 if you've got that many players) joining back in will join back in on Casual (or whatever difficulty they picked in step 1). They aren't given a choice about what difficulty they want to join in on. In addition to this I have no idea about what difficulty they'll be on if they join a game in progress that they've not played in before but since it has no impact on getting the star achievements I haven't bothered to find out.What you get
Player 1 gets 3 Onyx stars, a Declassified Mission completed on Insane and progress towards beating the campaign on Insane.
Player 2 gets 3 Onyx stars
This may not seem so good but it means that your 2nd playthrough for player 2 only requires that they beat the Declassified Mission on Insane - stars aren't important. This means you can have as many DBNOs (down but not out) during the mission as you like and as long as you live through it you'll get the credit for doing it. Another bonus is that player 2 doesn't have to quit out when you finish the declassified missions on that 2nd playthrough meaning everyone can stay in the game and earn XP.
I credit DarkxMaterials for the solution that told me about the co-op trick in the first place.
I'm taking the credit for figuring out that everyone can get the stars at the same time though