Insane is not available until you complete Hardcore. However, you can play Insane if you join a co-op match hosted by someone who has beaten Hardcore. The easiest way to get all the achievements besides the multiplayer ones is to join an Insane co-op game from the start. It'll take you maybe 6 hours to complete the game, and you'll get every non-multiplayer achievement except "Clusterluck", "Prison Breakout", and the three cog tag ones. (See "For the Fallen").
You can play this in co-op, single player, or a mixture of both, as long as you have credit for completing each individual chapter on Insane.
For tips on defeating General RAAM, see "A Dish Best Served Cold"
For a complete walkthrough, check this guide.