I believe that at least one of these achievements does stack from game to game. I just got the Death Rain achievement on the squid boss level. I had played through the game once before and tossed a lot of guys over the edge in the first couple levels.
On my second play through I did not toss anyone until the squid level and I was keeping count while I was tossing guys overboard. I got the achievement when I hit around 35 so this one definitely adds up from game to game. Not sure about any others though.