WW$^{R}$ means even length palindrome so its complement must accept
1) Odd length string
2) Even length string which are not palindrome
So here we can get help of non determinism we perform push and at arbitrary point X assuming it to be half of string now we pop so there are few possibility
1) at least one symbol did not match (success)
2) Stack is empty and no input string is remaining to read (failure)
case 1 is definitely true for odd length string thus accepting but it also help in accepting even length string which are not palindrome.
case 2 is true when string is even length palindrome so thus at the end we will make an transaction to non final state