You'll need Java 8 64-bit from http://www.oracle.com/technetwork/java/javase/downloads/jre8-downloads-2133155.html
Get the Technic Launcher from http://www.technicpack.net/download, run it, install, login with your Minecraft Username/Password, search for "Atlantica" in MODPACKS, install the one with the Ariel logo.
Set it to 2.5GB in the "Launcher Options" and "JAVA SETTINGS" on the Technic Launcher. (It will run with as little as 1GB if you must run it with less.)
Click the Play button to start the modpack.. The server to play on will already be listed in the Multiplayer screen in Minecraft.
Platform URL: http://api.technicpack.net/modpack/atlantica