Here's your approach:
Read both input strings.
Loop through each character position (both strings have equal length).
Convert both characters at position to lowercase using tolower().
Compare the lowercase characters. If the first string's character is smaller, output -1 and exit. If the second is smaller, output 1 and exit.
If you finish the loop without finding a difference, the strings are equal. Output 0. The approach is converting each pair of characters before comparing. Don't convert the entire string at once. Process character-by-character and return early when you find a difference.