If you have any doubts that this is your typical silver-age comic, the splash page doesn't let them remain. On it you see Aquaman, Aqualad, and some lady being threatened by flying submarines (yeah, flying subs!). During the silver-age, the splash page showed what would happen in the middle of the comic (always a situation where Aquaman's life was threatened), so that's not how the story begins.
It begins with Aquaman (with Aqualad) on his way to investigate an abandoned ship, and to take it to a shore so it would not collide with another ship. But a gigantic water form comes out of nowhere and grapples Aquaman and Aqualad.
When they get free, the form dissolves back into water, and they see a wave in the form of big lens above the ship that is collecting solar rays and burning the ship. The ship explodes and Aquaman and Aqualad spot a human figure swimming away from the remains of the ship. As they approach the figure, she takes flight inside of a solid water bubble, but it collapses as soon as it's about 20 feet above water.
By this time Aquaman and Aqualad had discerned that it was a female figure inside the bubble. When she collapsed, almost unconscious, Aquaman leaped to grab her. She tells them she lost her powers and begs them not to hurt her. Suspicious at first, Aquaman and Aqualad let her explain what she was doing there, as they thought she was the one who exploded the ship. She tells them that this is not so, that she saved the crew with her hard-water powers. She explains that she is a queen, Mera, from another dimension and that, after some time as queen, some bad guys, led by Leron, were planning to take away her throne. So she escaped to this dimension via a dimensional gateway constructed by her dimension's most brilliant scientist, and it is only a matter of time before Leron would gain her throne. Believing her, Aquaman says he will take care of her, and help her while in this dimension.
The threesome are then attacked by flying subs, dodge them, and discover that it is Leron and his gang, who had followed Mera to this world. With his powers, Leron traps Aquaman, Aqualad and Mera in ice. Gaining some time by talking with Leron, Aquaman is able to call his finny friends to help him, freeing the three of them while Leron and his gang swim away, swearing that when they come back they will be reinforced and ready to kill all of the three.
Aquaman leaves Mera with Aqualad, telling them he has a plan, and to wait till he comes back. But while Mera shows Aqualad where the gateway is, Leron returns and sends them spinning into a subterranean tunnel. Aquaman appears in the nick of time and saves them by mimicking Leron's powers with the help of the hidden Quisp, the other-dimensional imp. The defeated Leron swims away again.
Aquaman tells Quisp to go to his dimension and call an army of imps like him to defeat Leron once and for all, but Leron hears it (he is disguised as a shark) and attacks Quisp by surprise, leaving him unconscious. Then, along with his gang, he captures Aquaman, Aqualad and Mera once again and takes them to his dimension, where he plans to use Mera as a tool to convince the scientist to tell him how to control the dimension gateway. But Aquaman calls his finny friends, who free them, and they return to Earth. Upon returning, Aquaman cleans Mera's arm of a big spot of oil.
When Leron comes back to try to trap them again, Mera repels him using her returned powers. Aquaman, perceiving that there is a connection between the oil and Mera's powers, goes to a ship carrying oil and strikes its tank (!), spreading oil in the water. Leron and his gang are caught in the oil, and lose their powers. They are easily captured. Mera says, surprised, that she didn't understand why her powers were gone when she had oil in her arm, as only lead could remove her powers. Aquaman replies that almost all refined oil has a percentage of lead in it.
Mera returns to her dimension as the gateway is closing. Aquaman talks to Quisp, who has recovered, and says that he probably will see her again. Which he definitely did...
Review contributed by Rodrigo Mariath Zeidan