The Juggernaut will be unlocked by a technology which requires Citadels and Battleships to be already researched. A Starbase will also need to have a Colossal Assembly Yard in order to be able to construct one. The Colossal Assembly Yard is required for (and unlocked by) both the Colossus and the Juggernaut.

How strong is a juggernaut Stellaris?

The Juggernaut only has as much firepower as ~2.5 battleships. Not reasonable to expect it to beat that. It exists primarily to be a mobile repair/shipyard. It would be more useful if you couldn't use enemy starbases to repair at.

What DLC do you need for juggernaut Stellaris?

Stellaris - Juggernaut technology indirectly requires Apocalypse DLC.