Tulip has successfully integrated with Epicor in the past. When it comes to Epicor integrations, most customers use the Epicor Web API to transact with Tulip.
The Epicor API documentation is only officially available to paying customers, and therefore, you need to contact your internal Epicor team or your Epicor Salesperson for the documentation.
This type of integration does require substantial involvement from the internal team that manages your Epicor deployment.
However, if you have their support, you should check out our guide to HTTP connectors to get you started.