Servlet Filter: How to get all the headers from servletRequest?

Typecast ServletRequest into HttpServletRequest (only if ServletRequest request is an instanceof HttpServletRequest).

Then you can use HttpServletRequest.getHeader() and HttpServletRequest.getHeaderNames() method.

Something like this:

@Override
public void doFilter(ServletRequest request, ServletResponse response, FilterChain chain) throws IOException, ServletException {
    HttpServletRequest httpRequest = (HttpServletRequest) request;
    Enumeration<String> headerNames = httpRequest.getHeaderNames();

    if (headerNames != null) {
            while (headerNames.hasMoreElements()) {
                    System.out.println("Header: " + httpRequest.getHeader(headerNames.nextElement()));
            }
    }

    //doFilter
    chain.doFilter(httpRequest, response);
}

With Java 8+ you can use a stream to collect request headers:

HttpServletRequest httpRequest = (HttpServletRequest) request;

Map<String, String> headers = Collections.list(httpRequest.getHeaderNames())
    .stream()
    .collect(Collectors.toMap(h -> h, httpRequest::getHeader));

UPDATED

@Matthias reminded me that headers can have multiple values:

Map<String, List<String>>

Map<String, List<String>> headersMap = Collections.list(httpRequest.getHeaderNames())    
    .stream()
    .collect(Collectors.toMap(
        Function.identity(), 
        h -> Collections.list(httpRequest.getHeaders(h))
    ));

org.springframework.http.HttpHeaders

HttpHeaders httpHeaders = Collections.list(httpRequest.getHeaderNames())
    .stream()
    .collect(Collectors.toMap(
        Function.identity(),
        h -> Collections.list(httpRequest.getHeaders(h)),
        (oldValue, newValue) -> newValue,
        HttpHeaders::new
    ));

https://gist.github.com/Cepr0/fd5d9459f17da13b29126cf313328fe3

You should consider that the same HTTP header can occur multiple times with different values:

Map<String, Serializable> headers = Collections.list(request.getHeaderNames()).stream().collect(Collectors.toMap(h -> h, h -> {
    ArrayList<String> headerValues = Collections.list(request.getHeaders(h));
    return headerValues.size() == 1 ? headerValues.get(0) : headerValues;
}));