Here's what i've tried to do but it gives me HTTP code 500

Most likely because you're sending the wrong data in a mixture of wrong formats with the wrong type:

• You're using multipart form data, not JSON
• You're then setting the request parameter as a JSON string (q)
• The JSON string you're using in q isn't even valid (it's at least missing an opening curly brace) - and handwriting JSON is almost universally a bad idea, leverage a framework to do it for you instead.

Instead, the normal thing to do would be to create a POJO structure that maps to your request, so:

public class CrawlRequest {

    private CrawlInnerRequest request;
    @JsonProperty("spider_name")
    private String spiderName;

    //....add the getters / setters
}

public class CrawlInnerRequest {

    private String url;
    private String callback;
    @JsonProperty("dont_filter")
    private String dontFilter;

    //....add the getters / setters
}

...then simply create a CrawlRequest, set the values as you wish, then in your post call use:

.body(BodyInserters.fromValue(crawlRequest))

This is a rather fundamental, basic part of using a WebClient. I'd suggest reading around more widely to give yourself a better understanding of the fundamentals, it will help tremendously in the long run.

Don't we have onStatus()?

    public Mono<Void> cancel(SomeDTO requestDto) {
        return webClient.post().uri(SOME_URL)
                .body(fromObject(requestDto))
                .header("API_KEY", properties.getApiKey())
                .retrieve()
                .onStatus(HttpStatus::isError, response -> {
                    logTraceResponse(log, response);
                    return Mono.error(new IllegalStateException(
                            String.format("Failed! %s", requestDto.getCartId())
                    ));
                })
                .bodyToMono(Void.class)
                .timeout(timeout);
    }

And:

    public static void logTraceResponse(Logger log, ClientResponse response) {
        if (log.isTraceEnabled()) {
            log.trace("Response status: {}", response.statusCode());
            log.trace("Response headers: {}", response.headers().asHttpHeaders());
            response.bodyToMono(String.class)
                    .publishOn(Schedulers.elastic())
                    .subscribe(body -> log.trace("Response body: {}", body));
        }
    }