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"
# who has this hope fixed on him
Here to have hope is to confidently expect something good. Alternate translation: "who confidently expects this because of Christ" or "who confidently waits in Chrsit for this"
# who has this hope fixed on him
The phrase "this hope" refers to the hope of being like Christ, as mentioned in the previous verse. Alternate translation: "who confidently expects in Christ to become like Christ" or "who confidently waits for Christ to cause him to become like Christ"