Well I see a non-regex way to go about it:
public boolean isValidPassword(String s) {
    int lowerCase = 0;
    int upperCase = 0;
    int numeric = 0;
    int special = 0;
    for (int c = 0; i < s.length(); i++) {
        char i = s.charAt(c);
        if (i >= 'A' && i <= 'Z') {
            upperCase++;
        } else if (i >= 'a' && i <= 'z') {
            lowerCase++;
        } else if (i >= '0' && i <= '9') {
            numeric++;
        } else {
            special++;
        }
        //early ending case
        return lowerCase > 1 && upperCase > 1 && numeric > 0;
    }
    return false;
}
If you wanted to you could abstract the early ending predicate using a functional interface:
@FunctionalInterface
private static interface PasswordMatch {
    public boolean match(int lowerCase, int upperCase, int numbers, int special);
}
public boolean isValidPassword(String s, PasswordMatch matcher) {
    //...
        //in loop
        if (matcher.match(lowerCase, upperCase, numeric, special) {
            return true;
        }
    //...
}
Thus making the call mutable to the situation:
if (isValidPassword(/* some pass */, (lower, upper, number, spec)
                -> lowerCase > 1 && upperCase > 1 && numeric > 0)) {
    //etc...
}