As far as my limited skills can determine, you have basically two options:

• Make your regex include all possible 3-out-of-4 permutations and separate them with "or" using |
• Split your matches out into separate regexes, and count how many of them match.

Neither is particularly brief, but I think the latter is more concise and readable. Here's my example of that solution:

if (3 <= scalar grep { $str =~ /$_/ } ( # Match at least 3 of:
    qr/^.*(?=.{10,})(?=.*\d).*$/,
    qr/^.*(?=.{10,})(?=.*[a-z]).*$/,
    qr/^.*(?=.{10,})(?=.*[A-Z]).*$/,
    qr/^.*(?=.{10,})(?=.*[@#$%^&+=]).*$/
   )
) {
    # Do something.
}
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