public class ApiDependencyResolver : IDependencyResolver
    {
        public ApiDependencyResolver(IWindsorContainer container)
        {
            Container = container;
        }

        public IWindsorContainer Container
        {
            get;
            private set;
        }

        public object GetService(Type serviceType)
        {
            try
            {
                return Container.Kernel.HasComponent(serviceType) ? Container.Resolve(serviceType) : null;
            }
            catch (Kernel.ComponentNotFoundException)
            {
                return null;
            }
        }

        public IEnumerable<object> GetServices(Type serviceType)
        {
            try
            {
                return Container.ResolveAll(serviceType).Cast<object>();
            }
            catch (Kernel.ComponentNotFoundException)
            {
                return Enumerable.Empty<object>();
            }
        }
        public IDependencyScope BeginScope()
        {
            return new SharedDependencyResolver(Container);
        }

        public void Dispose()
        {
            Container.Dispose();
        }
    }

    public class SharedDependencyResolver : IDependencyScope
    {
        public SharedDependencyResolver(IWindsorContainer container)
        {
            Container = container;
            Scope = Container.BeginScope();
        }

        public IWindsorContainer Container
        {
            get;
            private set;
        }

        public IDisposable Scope
        {
            get;
            private set;
        }

        public object GetService(Type serviceType)
        {
            try
            {
                return Container.Kernel.HasComponent(serviceType) ? Container.Resolve(serviceType) : null;
            }
            catch (ComponentNotFoundException)
            {
                return null;
            }
        }

        public IEnumerable<object> GetServices(Type serviceType)
        {
            try
            {
                return Container.ResolveAll(serviceType).Cast<object>();
            }
            catch (ComponentNotFoundException)
            {
                return null;
            }
        }

        public void Dispose()
        {
            Scope.Dispose();
        }
    }

public IDependencyScope BeginScope()
{
    var child = container.CreateChildContainer();
    return new ApiDependencyResolver(child);
}

public class KernelInstaller : IWindsorInstaller
    {
        public void Install(IWindsorContainer container, IConfigurationStore store)
        {          
           container.Register(Classes.FromThisAssembly().BasedOn<ApiController>().LifestyleTransient());         
            container.Kernel.Resolver.AddSubResolver(new CollectionResolver(container.Kernel, true));
        }
    }

public class Startup
    {
        public void Configuration( IAppBuilder appBuilder )
        {
           var container = new WindsorContainer();
            container.Install(new KernelInstaller());

            var config = new HttpConfiguration
            {
                 DependencyResolver = new ApiDependencyResolver(container)
            };                  

            config.MapHttpAttributeRoutes();

            config.Routes.MapHttpRoute(
                name: "Default" ,
                routeTemplate: "{controller}/{action}/{name}" ,
                defaults: new { name = RouteParameter.Optional }                
            );

            config.EnsureInitialized();          
         
            appBuilder.UseWebApi( config );
        }
    }