...he was a full-fledged alien hunter, with his partner, the Boy Wonder, Robin!
In the collection of 80 Page Giant Magazine #12 of July, 1965, the Dynamic Duo faced many an alien invasion, from the Strange Worlds Of Batman and Robin.
Take a look at the stories....
Detective Comics #256
The captive planet is Tora, and Batman and Robin have to work to free captives to fight against alien invaders to this world. Under the leader Boran, the dynamic duo destroy a machine holding prisoners helpless. Torans and Earthlings unite, to fend off the invaders, with Batman. Robin and everyone else from Earth being able to return home.
Bruce Wayne decides to help archeologist William Sayre, who says he found cave drawings of dinosaurs by cavemen (who didn't exist at the same time). Enlisting the help of Professor Carter Nichols, Batman and Robin travel back in time via hypnosis (it was the 1950s....). The dynamic duo meet a caveman with a secret identity, that of Tiger Man. Working with Tiger Man, Batman and Robin defeat a villain named Borr (who has a secret weapon, that of a dinosaur frozen in ice). The dinosaur gets free from the ice after Batman starts a fire, but dies quickly after. Tiger Man promises to immortalize the events on cave wall, and Batman and Robin return to the present.
Batman and Robin end up in another dimension while chasing a criminal, with Batman joining a competition after finding out a resident was fixing the game. Winning, Batman ends up being crowned King of Plaxius, where the criminal Batman was following, Gurney, finds out Batman's secret identity, and then gets Batman dethroned and imprisoned. Selina, the girlfriend of Vol, Praxius' hero, frees Bruce, and they free Vol and defeat Rakk. Batman and Robin still have to deal with Gurney revealing Batman's secret identity, until they lose their memories returning to Earth.
That is, the dynamic duo face a plot that is similar to the old nursery rhyme, "There Was A Crooked Man".
World's Finest Comics #91
The World's Finest trio chase a criminal into a mountain cave, where the thug traps them with knockout gas and Kryptonite. The three heroes wake up a thousand years later, with the inhabitants looking use their time-ray to send the heroes to their home time.....except they are unable to since the device was stolen. The trio face off against Rohtul, a descendant of Luthor, defeating him, but not finding the time-ray. Batman figures out that Lora, one of the scientists, was really behind the theft of the time-ray, travel back in time, and prevent the criminal from sealing them in the cave.
This time around, Professor Nichols was lost in ancient Rome, with Batman and Robin having to travel back to find him. The dynamic duo find the Professor being held by Roman King Phorbus, ending up being captured...thought they make a giant balloon to escape, then the team go back to free Nichols and return to their home time.
Alien Kraak, lands on Earth, getting help from Batman and Robin, as he is being chased by other aliens. Only problem is, Kraak was a space pirate, and they capture Batman and Robin as criminals for the dynamic duo's honest mistake. Batman helps Kraak escape, then they go to collect his stolen loot from the dangerous Forest of Peril. Kraak tries to double cross Batman, but Batman was working with the local police of Ergon, who end up arresting Kraak and his associates for their crimes.
Batman and Robin are flying in the Batplane when a hurricane throws them into another dimension, where they are mistaken for Bat-People and taken prisoner by the local queen. Batman saves the queen from the Bat-People when they attack, and helps her find a traitor in her midst, her advisor, Arko. Finding a local deposit of coal, Batman lights it on fire, with the hope the flames will ward off the Bat-People for years. The explosion from this hurtles the Batplane with Batman and Robin home.
The Batman stories aren't as out of touch with modern Batman stories, as writer Grant Morrison used Batman's meeting with Professor Milo from Batman #112 (and other stories from the 1950s collected in Batman: The Black Casebook of 2009) for a series of stories he did in the 21st Century for his Batman R.I.P. storyline.