This achievement is self explanatory. You need to destroy 50 capital ships. It should be noted that only frigates, warships, cruisers, haulers and freighters add towards the total. Fighters, Pirate Lords and small cargo ships do not.
Unsure what class of ship something is? While in your craft, press
to pull up your action wheel. Place your cursor over a ship and details will show up including class (type of ship), faction (The ship's alliance), posture (whether a ship is peaceful or hostile), bounty (And how much they're worth if you destroy them) and finally what their cargo is.
If you wish to see your progress towards the achievement, go into your PDA
until you arrive at the system tab, then select "stats" and you can view the number of capital ships you have destroyed.