gistfile1.txt

scala> import Implicits._
import Implicits._

scala> FirstEvent("hello")
res0: FirstEvent = FirstEvent(hello)

scala> res0.handle
res1: String = hello

scala> ThirdEvent("hello")
res2: ThirdEvent = ThirdEvent(hello)

scala> res2.handle
<console>:18: error: could not find implicit value for parameter handler: EventHandler[ThirdEvent,U]
       res2.handle
            ^

tc.scala

trait Event

case class FirstEvent(firstHello: String) extends Event
case class SecondEvent(secondHello: String) extends Event
case class ThirdEvent(thirdHello: String) extends Event

trait EventHandler[T <: Event, U] {
  def handle(event: T): U
}

object EventHandler {
  implicit object FirstEventHandler extends EventHandler[FirstEvent, String] {
    def handle(t: FirstEvent) = t.firstHello
  }

  implicit object SecondEventHandler extends EventHandler[SecondEvent, String] {
    def handle(t: SecondEvent) = t.secondHello
  }
}

object Implicits {
  implicit class EventHandlerSyntax[T <: Event](event: T) {
    def handle[U](implicit handler: EventHandler[T, U]): U =
      handler.handle(event)
  }
}