How do I remove every message from players e.g. Was killed by Xy or did the first man open his inventory
So. The death news ends with "/ gamerule showDeathMessages false".
The achievements go out in the server.properties (if server). In 1.8.8 it would be the value "announce-player-achievements = true", simply change to "announce-player-achievements = false".
The easiest way to do it is with this command
/ gamerule showDeathMessages false
/ gamerule showdeathmessages false