CERTIFICATION PURSUANT TO SECTION 302 OF THE
SARBANES-OXLEY ACT OF 2002

I, Andrew Marshall, certify that:

|1. | I have reviewed this annual report on Form 40-F of First
      Mining Finance Corp.;                                                                                                                                                                                                                                                                
|-- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
|   |                                                                                                                                                                                                                                                                                                                                                     
|2. | Based on my knowledge, this report does not contain any
      untrue statement of a material fact or omit to state a material fact
      necessary to make the statements made, in light of the circumstances under
      which such statements were made, not misleading with respect to the period
      covered by this report;                  
|   |                                                                                                                                                                                                                                                                                                                                                     
|3. | Based on my knowledge, the financial statements, and
      other financial information included in this report, fairly present in all
      material respects the financial condition, results of operations and cash
      flows of the issuer as of, and for, the periods presented in this
      report;                                         
|   |                                                                                                                                                                                                                                                                                                                                                     
|4. | The issuers other certifying officer and I are
      responsible for establishing and maintaining disclosure controls and
      procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and
      internal control over financial reporting (as defined in Exchange Act
      Rules 13a-15(f) and 15d-15(f)) for the issuer and have:
|   |                                                                                                                                                                                                                                                                                                                                                     
|   | (a)                                                                                                                                                                                                                                                                                                                                                 
|   |                                                                                                                                                                                                                                                                                                                                                     
|   | (b)                                                                                                                                                                                                                                                                                                                                                 
|   |                                                                                                                                                                                                                                                                                                                                                     
|   | (c)                                                                                                                                                                                                                                                                                                                                                 

|   | (d)                                                                                                                                                                                                                                                                                                         | Disclosed in this report any change in the issuers
      internal control over financial reporting that occurred during the period
      covered by the annual report that has materially affected, or is
      reasonably likely to materially affect, the issuers internal control over
      financial reporting; and
|-- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
|   |                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                           
|5. | The issuers other certifying officer and I have
      disclosed, based on our most recent evaluation of internal control over
      financial reporting, to the issuers auditors and the audit committee of
      the issuers board of directors (or persons performing the equivalent
      functions):
|   |                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                           
|   | (a)                                                                                                                                                                                                                                                                                                         | All significant deficiencies and material weaknesses in
      the design or operation of internal control over financial reporting which
      are reasonably likely to adversely affect the issuers ability to record,
      process, summarize and report financial information; and                                   
|   |                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                           
|   | (b)                                                                                                                                                                                                                                                                                                         | Any fraud, whether or not material, that involves
      management or other employees who have a significant role in the issuers
      internal control over financial reporting.                                                                                                                                        

Date: April 19, 2017

/s/ Andrew
      MarshallAndrew MarshallChief Financial Officer(Principal Financial Officer and) PrincipalAccounting Officer