architecture - How to handle collisions without ugly conditionals and type checking?

_{(I asked a similar question, but this one is far more specific).}

How can I handle collisions without having to do a lot of type checking and if statements?

People here suggested that when spotting a collision, the collision detector should notify both entities in the collision, and the entities themselves will encapsulate the logic to react to the collision.

I like the idea of having the entities themselves decide how to handle the collisions. However I'm not sure how to avoid doing a lot of type checking and if statements inside the handleCollision methods.

For example (in psuedocode):

class CollisionDetector{
    foreach entity in entities
        foreach otherEntity in entities
            if(collision(entity,otherEntity)) entity.handleCollision(otherEntity);
}

class Entity{
    // .. stuff omitted
    void abstract handleCollision();

}

class Alien extends Entity{
    // .. stuff omitted
    void handleCollision(Entity entity){
        // lots of ugly conditionals and type checking
        if(entity instanceof Missile) die();
        if(entity instanceof Alien) lifePoints -= ((Alien)entity).getDamagePoints();
        if(entity instanceof Wall) setVelocity(0,0);
        // .. etc

    }
}

In OOP we should try to avoid type checking and employ Polymorphism. But I don't see how this can be done in this case.

Is there a way to avoid the ugly type checking and lots of conditionals? Or should I just make my peace with it? How is this most commonly done?