How can we do a software load balancing using API gateway on their target end point? This feature is available in Apigee and looking for the same in API Gateway.
Please check if Load Balancing Routing policy will satisfy your requirements.
Presumably you’ve considered an option to implement the load balancing on a network device (like F5 BIG-IP LTM or equivalent) and not on the API Gateway. The API GW can do it but the LB function may be more appropriate hosted elsewhere so that other traffic, not just API calls, can benefit from the LB capability.