Here's Bungie's post about what is staying and what's going.
https://www.bungie.net/en/Explore/Detail/News/49454Achievement wise, the only thing that will no longer be obtainable are the two related to the Leviathan raid in the base game. Others may become more difficult, but those two (beat Leviathan, beat Leviathan in Prestige) are the only ones that will not be possible. Of course, it's always possible they change the reqs and just make you beat any raid instead of Leviathan.