// Introduce a flip method: it looks tricky, but as usual it just "follows the types":
private def flip[L, R](eitherFuture: Either[L, Future[Either[L, R]]]): Future[Either[L, R]] = {
  eitherFuture.fold[Future[Either[L, Either[L, R]]]](
    left => Future.successful[Either[L, Either[L, R]]](Left(left)),
    right => right.map(Right(_))
  ).map(_.joinRight)
}

// Now we can count on flapMap to do the magic!
def processRequest(a: A): Future[Result] = {
  for {
    b <- f1(a)
    c <- flip(b.map(f2))
    d <- flip(c.map(f3))
    r <- flip(d.map(f4))
  } yield r.getOrElse[Result](r.left.get)
}