In Batman #130, Batman and Robin faced The Hand From Nowhere, which was controlled by two apparent aliens:
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Status: Fake aliens; in fact it's a criminal gang led by longtime Superman foe, Luthor.
In Batman #132, the dynamic duo meet a man from Mars:
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Status: Another fake alien; Karik was actually an actor playing a part who suffered the dreaded "blow to the head" that made him think he was really from Mars.
In Batman #136, Batman and Robin repel an Vordian invasion force:
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Status: True aliens, human sized and yellow in color. Two Klaatus out of a possible five.
In Detective #277, an alien ship crash-lands on Earth:
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Status: True alien, human-sized and orange in color. His crash landing frees the Jigsaw Puzzle Creature. Three Klaatus out of five.
Detective #279 features these:
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Status: A very tough call. The robot-looking thing is a robot and the orange and pink creature is a beast, with only rudimentary intelligence. In addition, they are from another dimension, which also makes things trickier as I've not included Bat-Mite, for example, as an alien in my schema. I'm going to rule against the true alien nature here as even a robot has no real intelligence.
In Detective #282, we first meet Batman's Interplanetary Rival, Tal-Dar, chief of the Interplanetary Space Police:
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Status: True alien, orange and human-sized. As the only alien who appeared in two separate Batman stories (other than Superman of course), Tal-Dar, who later popped up in Batman #142 gets the full five Klaatus.
We also meet another alien race in the story:
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Status: True aliens, human-sized and green. Two Klaatus.
In Detective #283, a crooked scientist summons an alien to Earth with a machine:
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Status: True alien, white and human-sized. Three Klaatus for DC daring to reuse the Martian Manhunter's origin in a Batman story in Detective.
It certainly looks like 1960 was another banner year for aliens in the Batman canon. Summary for 1960:
Batman #130: Fake aliens
Batman #132: Fake aliens
Batman #136: True aliens, yellow and human-sized
Detective #277: True alien, orange and human-sized
Detective #279: Not a true alien, rather alien robot and alien beast
Detective #282: True aliens (two races): one orange and one green, both human-sized
Detective #283: True alien, white and human-sized
Overall for the year: Four stories with true aliens, one with an alien robot and an alien beast, and two stories with fake aliens.
1961:
Batman #137: True alien, white and human-sized and true aliens, yellow and human-sized (two separate stories).
Batman #140: Superman appearance; not counted in the tabulation, and true aliens, green and human-sized.
Batman #142: True alien, orange and human-sized.
Batman #143: Not a true alien, an alien beast.
Batman #144: True aliens, yellow and human-sized.
Detective #287: True aliens, one white and the other yellow, both slightly smaller than humans.
Detective #291: Not a true alien, an alien beast.
Detective #292: Superman cameo, not counted in the tabulation.
Detective #293: True aliens, pink and oversized.
Detective #295: True aliens, yellow and human-sized.
So in total we have 8 stories with true aliens (counting both stories in Batman #137), two stories with alien beasts and two Superman stories.
1962:
Detective #299: True aliens, several, green or white, human-sized.
Detective #303: Fake aliens.
Batman #148: True aliens, green and human-sized
Detective #305: True alien, orange and human-sized
Batman #152: Fake alien.
Three real aliens, two fake aliens.
1963-1964:
Batman #153: True aliens, green.
Batman #153: True aliens, multi-colored.
Batman #156: Fake alien (dream sequence)
Detective #320: No alien visible but implied.
Batman #160: Fake Alien
Two real aliens, two fake, one not seen.
I try to mention when I remember it, that these types of posts are very much inspired by H at the Comic Treadmill, whose terrific prop stars series are highly recommended.