To obtain the Battacor you will have several options, being the first one to buy it in the Market console or through the Arsenal for 175 Platinum. If you choose this way, you also get an Orokin Catalyst already installed, as well as an extra weapon slot in your Arsenal. It is not the cheapest option, but it is the fastest and direct, only available for those willing to pay all this Platinum.
The second option to obtain the Battacor is completing the Corpus lab Research in your Dojo. When you complete the Research you will have access to the Bluperint to buy it and craft it in the Foundry of your ship.