Exhibit 5.1

Hyperion DeFi, Inc.

23461 S. Pointe Drive, Suite 390

Laguna Hills, CA 92653

Ladies and Gentlemen:

We have acted as counsel to Hyperion DeFi, Inc., a Delaware corporation (the “Company”), in connection with the registration by the Company under the Securities Act of 1933, as amended (the “Securities Act”), pursuant to the Company’s Registration Statement on Form S-3, which was filed with the Securities and Exchange Commission on the date hereof (the “Registration Statement”), of the resale by the holders thereof of (i) up to 15,384,615 shares of common stock, par value $0.0001 per share (the “Common Stock”), of the Company issuable upon the conversion of 5,128,205 shares of the Company’s Series A Non-Voting Preferred Stock, par value $0.0001 per share (the “Series A Preferred Stock”), that were issued pursuant to the Securities Purchase Agreement, dated June 17, 2025, by and among the Company and certain institutional accredited investors (the “Securities Purchase Agreement”); (ii) up to 30,769,230 shares of Common Stock issuable upon the exercise of warrants (the “Purchaser Warrants”) at an exercise price of $3.25 per share, which Purchaser Warrants were issued pursuant to the Securities Purchase Agreement; (iii) up to 923,076 shares of Common Stock issuable upon the conversion of 307,692 shares of Series A Preferred Stock (together with the shares of Common Stock issuable upon the conversion of the shares of Series A Preferred Stock that were issued pursuant to the Securities Purchase Agreement, the “Conversion Shares”) that were issued pursuant to the Engagement Letter, dated June 17, 2025, by and between the Company and Chardan Capital Markets, LLC (the “Engagement Letter”); (iv) up to 1,846,153 shares of Common Stock issuable upon the exercise of warrants (the “Placement Agent Warrants”) at an exercise price of $3.25 per share, which Placement Agent Warrants were issued pursuant to the Engagement Letter; (v) up to 1,497,593 shares of Common Stock issuable as in-kind dividends on the Series A Preferred Stock (the “Dividend Shares”); and (vi) up to 350,000 shares of Common Stock issuable upon the exercise of warrants (the “Lender Warrants” and, together with the Purchaser Warrants and the Placement Agent Warrants, the “Warrants” and the shares of Common Stock issuable upon exercise of the Warrants, the “Warrant Shares”) at an exercise price of $4.00 per share, which Lender Warrants were issued in connection with the Fourth Amendment to the Supplement to the Loan and Security Agreement, dated November 22, 2022, with Avenue Capital Management II, L.P., as administrative agent and collateral agent, Avenue Venture Opportunities Fund, L.P., as a lender and Avenue Venture Opportunities Fund II, L.P., as a lender. The Conversion Shares, the Dividend Shares and the Warrant Shares are referred to herein collectively as the “Issuable Shares.”

We have reviewed (i) the Registration Statement; (ii) the Securities Purchase Agreement; (iii) the Certificate of Designation of Preferences, Rights and Limitations of Series A Non-Voting Convertible Preferred Stock (the “Certificate of Designation”); (iv) the Engagement Letter; (v) the Warrants; and (vi) such corporate records, certificates and other documents, and such questions of law, as we have deemed necessary or appropriate for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals.

Hyperion DeFi, Inc.

July 18, 2025

Page 2

We have assumed that any Issuable Shares, when issued, will be duly registered on the books of the transfer agent and registrar of the Common Stock and that the Company will comply with applicable notice requirements regarding uncertificated shares provided under the Delaware General Corporation Law (the “DGCL”). We have assumed further that the information and representations and warranties contained in the agreements, instruments, records, certificates and other documents we reviewed were true, accurate and complete as of their stated date and are true, accurate and complete as of the date of this letter.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible. We express no opinion to the extent that, notwithstanding the Company’s current reservation of shares of Common Stock, future issuances of securities of the Company, including the Issuable Shares, and anti-dilution adjustments to outstanding securities of the Company, including the Series A Preferred Stock or the Warrants, may cause the Series A Preferred Stock or the Warrants to be convertible into or exercisable for more shares of Common Stock than the number that remain authorized but unissued. We also have assumed that the Conversion Price (as defined in the Certificate of Designation) and the Exercise Price (as defined in each of the Warrants) will not be adjusted to an amount below the par value per share of the Common Stock.

Based upon the foregoing, we are of the opinion that the Issuable Shares have been duly authorized and, when issued upon the conversion of or as in-kind dividends on the Series A Preferred Stock or upon exercise of the Warrants, as applicable, will be validly issued, and the Issuable Shares will be fully paid and non-assessable.

We are members of the bar of Commonwealth of Massachusetts and the State of New York. We do not express any opinion herein on any laws other than the DGCL.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus constituting part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Covington & Burling LLP