AMENDMENT NO. 1 TO REGISTRATION RIGHTS AGREEMENT

Exhibit 4.2

AMENDMENT NO. 1 TO REGISTRATION RIGHTS AGREEMENT

This Amendment No. 1 to Registration Rights Agreement (this “Amendment”), dated as of November 8, 2012, is made by Enduro Royalty Trust, a statutory trust formed under the laws of the State of Delaware (the “Trust”), and Enduro Resource Partners LLC, a Delaware limited liability company (the “Company”). Capitalized terms used but not defined herein shall have the meanings ascribed to them in the Agreement or the Amended and Restated Trust Agreement, as applicable (each as defined below).

WHEREAS, the Company and the Trust entered into that certain Registration Rights Agreement, dated as of November 8, 2011 (the “Agreement”), providing the Company certain registration rights with respect to the Trust Units held by the Company; and

WHEREAS, pursuant to Section 9(a) of the Agreement, the Agreement may be amended by written agreement signed by the Trust, without the consent of the Holders of Registrable Securities, to cure any ambiguity or to correct or supplement any provision contained therein that may be defective or inconsistent with any other provision contained therein, or to make such other provisions in regard to matters or questions arising under the Agreement that shall not adversely affect the interests of the Holders of Registrable Securities; and

WHEREAS, pursuant to Section 10.02 of the Amended and Restated Trust Agreement governing the Trust dated as of November 3, 2011 (the “Amended and Restated Trust Agreement”), the Trustee on behalf of the Trust may from time to time amend the Transaction Documents (as defined therein, and including the Agreement) to which the Trust (or the Trustee as trustee of the Trust) is a party, without the approval of Trust Unitholders in order to cure any ambiguity, or to correct or supplement any provision contained therein which may be defective, provided that any such supplement or amendment does not materially adversely affect the interests of the Trust Unitholders; and

WHEREAS, the Trustee is entitled to rely upon a certification of Enduro as conclusive evidence that any amendment or supplement described above is authorized and permitted under the Amended and Restated Trust Agreement and the other Transaction Documents and complies with the provisions of Section 10.02 of the Amended and Restated Trust Agreement; and

WHEREAS, the Company and the Trust have determined that the fourth recital in the preamble to the Agreement is defective, and the Trust desires to amend such recital in accordance with Section 9(a) of the Agreement and Section 10.02 of the Amended and Restated Trust Agreement, as set forth herein; and

WHEREAS, the Company has delivered a certificate to the Trustee to the effect that this Amendment is authorized and permitted under the Amended and Restated Trust Agreement and the other Transaction Documents and complies with the provisions of Section 10.02 of the Amended and Restated Trust Agreement.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and conditions herein set forth, the Trust and the Company hereby agree as follows:

Section 1. Amendments.

The fourth recital in the preamble to the Agreement is hereby amended and restated in its entirety to read as follows:

“WHEREAS, the Trust has agreed to file a registration statement or registration statements relating to the sale by the Company and its Transferees (as defined below) of the 19,800,000 Trust Units held by the Company after the Initial Public Offering (or such number of Trust Units held by the Company after giving effect to the Over-Allotment Option, if applicable) (the “Subject Units”).”

Section 2. Effect of Amendment. Except as expressly modified and amended herein, all of the terms and conditions of the Agreement shall remain in full force and effect.

Section 3. Governing Law. This Amendment shall be governed by, and construed in accordance with, the laws of the State of Delaware.

[Signature page follows.]

IN WITNESS WHEREOF, this Amendment has been signed by the Trust as of the day and year first above written.

[Signature Page to Amendment No. 1 to Registration Rights Agreement]