antipolice brutality marches or antipolice-brutality marches. Here's why:
Institutions like publishers and schools prepare or adopt style guides to codify how writing should be done to provide consistency while still communicating meaningfully. When it comes to writing narratives, there are several guides that you can turn to and generally find good advice for questions like this one.
There have been many specific questions about hyphen usage here, and it's worth while to review these style guides for their general recommendations and then see if there is an exception relevant to your specific question.
Let's start with the British Guardian and Observer Style Guide, where I'll emphasis some relevant points:
Our style is to use one word wherever possible. Hyphens tend to clutter up text (particularly when the computer breaks already hyphenated words at the end of lines). This is a widespread trend in the language: "The transition from space to hyphen to close juxtaposition reflects the progressive institutionalisation of the compound," as Rodney Huddleston puts it, in his inimitable pithy style, in his Introduction to the Grammar of English.
There is no need to use hyphens with most compound adjectives, where the meaning is clear and unambiguous without: civil rights movement, financial services sector, work inspection powers, etc.
Also use hyphens where not using one would be ambiguous, eg to distinguish "black-cab drivers come under attack" from "black cab-drivers come under attack". A missing hyphen in a review of Chekhov's Three Sisters led us to refer to "the servant abusing Natasha", rather than "the servant-abusing Natasha".
Prefixes such as macro, mega, micro, mini, multi, over, super and under rarely need hyphens
I could stop and summarize there, but let's look at an American style guide, the Chicago Manual of Style (drop down to #4 in that document):
Compounds formed with prefixes are normally closed, whether they are nouns, verbs, adjectives, or adverbs...(3) to separate two i’s, two a’s, and other combinations of letters or syllables that might cause misreading, such as anti-intellectual, extra-alkaline, pro-life;
anti: antihypertensive, antihero, but anti-inflammatory, anti-Hitlerian
(By the way, and I mentioned this in other answers referencing CMS. This appears to be a pdf taken from CMS. The CMS site requires registration.)
So, let's summarize:
The prefix anti is only hyphenated if the following word begins with i (or hi, possibly), based on (4), (5) and (6). This suggests that antipolice is recommended, rather than anti-police.
So now we have antipolice brutality march to consider. (2) says you don't need hyphens if the meaning is unambiguous, and (3) shows examples of how that ambiguity can be interpreted. There are two ways to look at it, and I'll use hyphens just to show associative grouping:
By (1) this is preferable: antipolice brutality marches, but is it ambiguous?
Otherwise, you need to use one of these to resolve the ambiguity:
Now I have never heard of brutality marches and I doubt anyone else has either, so I think you could safely go with no hyphens at all: antipolice brutality marches.
But if you want to be pedantic, or you think the risk of a pedant misunderstanding your meaning, then you probably should go with one of the hyphenated versions. I am confident the one with the correct meaning is antipolice-brutality marches.