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In Mars Attacks!, it's established that Martians must wear those space helmets because, unlike us oxygen-breathing Earthlings, Martians must breathe nitrogen.

Is this a deliberate joke by the writers or just research failure? Because, of course, Earth's atmosphere is mainly nitrogen!

Mars Attacks! the film was based on Mars Attacks, a set of trading cards (aka bubblegum cards) published by Topps in 1962.

The martians in the film are depicted with helmets because that's how they're depicted on the trading cards. Any other explanation is going to be an after-the-fact rationalization.

You can see images of the entire set of cards here. There's a paragraph on the back of each one explaining what each one was. None of the text directly addresses why the martians wear helmets on earth.

Cards 48 and later depict Martians on Mars living in domed cities, which could indicate that the Martian atmosphere is no longer ideal for their needs. But Martians are also shown outside the cities without helmets, so they can apparently operate in the martian atmosphere to some extent.

Humans are shown as needing breathing gear on Mars (with flak helmets on the inside, naturally), except for card 52 which is inside a Martian city.

We have confirmation from the film's official novelisation that these helmets are linked to a "life support backpack". It stands to reason that Earth's atmosphere, while containing nitrogen, isn't directly supportive of their form of life.

A dozen of Mars's finest marched in rows on either side of their
awesome Ambassador. These green creatures' long legs and arms were
ringed with jointed metal tubing. Their chests were crisscrossed with
flexible hoses that joined domed helmets to life-support backpacks.
The Martians carried toylike contraptions of tubes and spheres.

Based on the fact that the Martian infiltrator was able to survive by chewing a gum that was comprised of compressed nitrogen gas would suggest that the goal of the helmets is to provide an exclusively nitrogen (100%-ish) gas breathing environment and to exclude gases in Earth's atmosphere that would be poisonous to a Martian.

Mars atmosphere versus Earth atmosphere...

1. Mars atmosphere is known to be much thinner than the oxygen/nitrogen rich Earth atmosphere, I think, containing mostly carbon dioxide, (anyone with more accurate knowledge feel free to correct me), so the inclusion of space helmets on the Martians in mars attacks is likely a reference to the fact that they are, well... hey, ... Martians.


2. If we reference the SF megatext different planets represent inimical environments to invaders/non locals, think of the the Martians in HG Wells' War of the Worlds being undone by Earth bacteria.


3. In the film itself, one Martian is shown chewing gum that gives off highly concentrated nitrogen (please correct me if I am wrong, it is a long time since I watched this...) indicating they breathe pure nitrogen and not an oxygen nitrogen mix and again emphasizing that the Martians are not from Earth.


4. Rule of funny, the space helmets are deliberately ridiculous. This is not a film that cleaves close to actual science despite the fact that it was intended to feature a cameo by Carl Sagan. The bottom line is it's meant to be a comedy and is somewhat slapstick in its approach. Logic and scientific accuracy will always take second place to what seems funny.