How to call the c# script from objective-C code in Unity?

You can use

UnitySendMessage("GameObjectName1", "MethodName1", "Message to send");

in which you fill your gameobject name which will receive this message and the message name.

You can implement your own delegate/event once you receive this message from native code. The limit of UnitySendMessage is when it arrives to Unity code, it is always 1 frame after you call this in native code. And it can only take string as parameter. But most of time it is not big problem.

The method to be used for this is UnitySendMessage. Have a look at Building Plugins for iOS

Have a look at: http://www.tinytimgames.com/2010/01/10/the-unityobjective-c-divide/ The bolg post shows a technique that uses KVO (Key Value Observation) and the PlayerPrefs to pass commands from unity to objective-c.

PlayerPrefs.SetString("Commands",
   String.Format("AwesomeCommand|{0}|{1}", awesome1, awesome2));

Universal plugin for unity for iOS that allow mixing C# with objective-C https://www.assetstore.unity3d.com/#/content/10310

Unity C#

var callbackClass = AKiOSMagic.CreateClass("MyCallbackClass", "NSObject");
callbackClass.AddMethod("methodWithArg:anotherArg:", (args)
{
    // do something...
    // args.GetObject(0);
    // args.GetObject(1);
});
callbackClass.RegisterClass();

Objective-C

[[NSClassFromString(@"MyCallbackClass") new] methodWithArg:@"arg1" anotherArg:@"arg2"]