The word "him" refers to Christ. Having hope fixed on Christ means expecting that because of Christ, what is hoped for will happen. Alternate translation: "Everyone who has this hope because of Christ" or "Everyone who trusts Christ to fulfill this hope"
The phrase "this hope" refers to the hope of being like Christ, as mentioned in the previous verse. Here to have hope is to confidently expect something good. Alternate translation: "who confidently expects in Christ to become like Christ" or "who confidently waits for Christ to cause him to become like Christ"