the achievement is you can get a MEWTWO
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If you're referring to what the guy infront of Cerulean cave is saying, the Great Achievement is bringing the Sapphire and Ruby to the man in the research center on One Island.
there is no cerulean cave in ruby
yes you need all 16 badges to get into cerulean cave.
You can access Cerulean Cave in SoulSilver after you get all 16 gym badges (Johto and Kanto).
once you beat the elite four go to island 1 and talk to the guy in the big Pokemon building/Pokemon center.He will then give you a mission to find 1ruby and 1 sapphere once you do that you wil be able to go to cerulean cave