To determine if a String contains an upper case and a lower case char, you can use the following:
boolean hasUppercase = !password.equals(password.toLowerCase());
boolean hasLowercase = !password.equals(password.toUpperCase());
This allows you to check:
if(!hasUppercase)System.out.println("Must have an uppercase Character");
if(!hasLowercase)System.out.println("Must have a lowercase Character");
Essentially, this works by checking if the String is equal to its entirely lowercase, or uppercase equivalent. If this is not true, then there must be at least one character that is uppercase or lowercase.
As for your other conditions, these can be satisfied in a similar way:
boolean isAtLeast8 = password.length() >= 8;//Checks for at least 8 characters
boolean hasSpecial = !password.matches("[A-Za-z0-9 ]*");//Checks at least one char is not alpha numeric
boolean noConditions = !(password.contains("AND") || password.contains("NOT"));//Check that it doesn't contain AND or NOT
With suitable error messages as above.