Better solution here: http://www.splinter.com.au/2014/09/10/afnetworking-error-bodies/

AFURLSessionManager+ErrorResponse.m

!!! There's a better solution here now, that doesn't require swizzling:
!!! http://www.splinter.com.au/2014/09/10/afnetworking-error-bodies/
!!! But i'll leave the below swizzling solution up for old time's sake


//  AFURLSessionManager+ErrorResponse.h
//  This hacks AFURLSessionManager so that it returns the error response in failure callbacks, in the error's userInfo.

// Usage:
// [mySessionManager POST:@"some_api_endpoint" parameters:params success:^(NSURLSessionDataTask *task, NSDictionary *responseObject) {
// 	...
// } failure:^(NSURLSessionDataTask *task, NSError *error) {
//     id responseObject = error.userInfo[kErrorResponseObjectKey];
//     ...
// }];

#import "AFURLSessionManager.h"

/// The NSError userInfo dictionary key for the responseObject.
#define kErrorResponseObjectKey @"kErrorResponseObjectKey"

@interface AFURLSessionManager (ErrorResponse)
@end


//  AFURLSessionManager+ErrorResponse.m

#import "AFURLSessionManager+ErrorResponse.h"

#import <objc/runtime.h>

@implementation AFURLSessionManager (ErrorResponse)

#pragma mark - Hooks into the VC lifecycle

/// Wrap the completion handler with a new handler that injects the response into an error's userInfo before calling the original handler.
- (NSURLSessionDataTask *)errorResponse_dataTaskWithRequest:(NSURLRequest *)request
                                          completionHandler:(void (^)(NSURLResponse *response, id responseObject, NSError *error))originalCompletionHandler {
    // This calls through to the original, really.
    return [self errorResponse_dataTaskWithRequest:request completionHandler:^(NSURLResponse *response, id responseObject, NSError *error) {

        // If there's an error, store the response in it if we've got one.
        if (error && responseObject) {
            if (error.userInfo) { // Already has a dictionary, so we need to add to it.
                NSMutableDictionary *userInfo = [error.userInfo mutableCopy];
                userInfo[kErrorResponseObjectKey] = responseObject;
                error = [NSError errorWithDomain:error.domain code:error.code userInfo:[userInfo copy]];
            } else { // No dictionary, make a new one.
                error = [NSError errorWithDomain:error.domain code:error.code userInfo:@{kErrorResponseObjectKey: responseObject}];
            }
        }
        
        // Call the original handler.
        if (originalCompletionHandler) {
            originalCompletionHandler(response, responseObject, error);
        }
    }];
}

#pragma mark - Swizzling

/// Do the swizzling at load time.
+ (void)load {
    ErrorResponse_MethodSwizzle(self, @selector(dataTaskWithRequest:completionHandler:), @selector(errorResponse_dataTaskWithRequest:completionHandler:));
}

/// Swizzle the method into place.
void ErrorResponse_MethodSwizzle(Class c, SEL origSEL, SEL overrideSEL) {
    Method origMethod = class_getInstanceMethod(c, origSEL);
    Method overrideMethod = class_getInstanceMethod(c, overrideSEL);
    if (class_addMethod(c, origSEL, method_getImplementation(overrideMethod), method_getTypeEncoding(overrideMethod))) {
        class_replaceMethod(c, overrideSEL, method_getImplementation(origMethod), method_getTypeEncoding(origMethod));
    } else {
        method_exchangeImplementations(origMethod, overrideMethod);
    }
}

@end