Navy battle stars were awarded to Navy combat units during WWII, Korean War, and Vietnam who successfully completed (i.e., they weren't sunk) combat war patrols, or saw combat action against the enemy. Granted, there were likely posthumous awards, but that's hardly gratifying.
Since then, the annual "Battle E" (Battle Efficiency) is awarded instead to the best combat units who have displayed superior battle efficiency in place of combat operations against the enemy.
This is due in large part to the fact that their haven't been any Naval campaigns or major Naval battles/combat action in over 40 years.
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By participation in a battle. The eligible ships are determined by the Department of the Navy and listed in a Naval Bulletin that lists the battles and the ships.
Battle leyte gulf
George Dewey.
Perhaps it is easier to say what the US navy did do during the Mexican War. They undertook:Bombardment of GuaymasBattle of MontereyBattle of MulegeBombardment of Punta SombreroFirst Battle of TabascoSecond Battle of TabascoFirst Battle of TuxpanSecond Battle of TuxpanThird Battle of TuxpanBlockade of VeracruzSiege of Veracruz
Japanese Navy and the US Navy
It was the first naval battle fought exclusively with airplanes.The Battle of the Coral Sea was a tactical win for the Imperial Japanese Navy and a strategic win for the US Navy.
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By participation in a battle. The eligible ships are determined by the Department of the Navy and listed in a Naval Bulletin that lists the battles and the ships.
The US Navy won the Battle of Midway in June 1942. Basically a battle between aircraft carriers of the USA and Japan. The US Navy won decisively and this was the turning point of the war in the Pacific.
Battle leyte gulf
Possibly the "Battle of Savo Island." At least one US commander committed suicide after that battle.
George Dewey.
Perhaps it is easier to say what the US navy did do during the Mexican War. They undertook:Bombardment of GuaymasBattle of MontereyBattle of MulegeBombardment of Punta SombreroFirst Battle of TabascoSecond Battle of TabascoFirst Battle of TuxpanSecond Battle of TuxpanThird Battle of TuxpanBlockade of VeracruzSiege of Veracruz
Perhaps it is easier to say what the US navy did do during the Mexican War. They undertook:Bombardment of GuaymasBattle of MontereyBattle of MulegeBombardment of Punta SombreroFirst Battle of TabascoSecond Battle of TabascoFirst Battle of TuxpanSecond Battle of TuxpanThird Battle of TuxpanBlockade of VeracruzSiege of Veracruz
Perhaps it is easier to say what the US navy did do during the Mexican War. They undertook:Bombardment of GuaymasBattle of MontereyBattle of MulegeBombardment of Punta SombreroFirst Battle of TabascoSecond Battle of TabascoFirst Battle of TuxpanSecond Battle of TuxpanThird Battle of TuxpanBlockade of VeracruzSiege of Veracruz
Perhaps it is easier to say what the US navy did do during the Mexican War. They undertook:Bombardment of GuaymasBattle of MontereyBattle of MulegeBombardment of Punta SombreroFirst Battle of TabascoSecond Battle of TabascoFirst Battle of TuxpanSecond Battle of TuxpanThird Battle of TuxpanBlockade of VeracruzSiege of Veracruz