If your struggling to get this trophy then it can be got very easily if you have 2 Playstations. If you've already got a division in division rivals then you'll have to delete your ultimate team and start a new one to get a new set of 5 division rivals qualification matches.
To get it I created 3 alternate accounts, the did the following matches
1) Alt 2 v Alt 1 (scored an own goal with Alt 1 then quit as Alt 1 giving the win to Alt 2)
2) Alt 3 v Alt 1 (scored an own goal with Alt 1 then quit as Alt 1 giving the win to Alt 3)
3) Alt 3 v Alt 2 (scored an own goal with Alt 2 then quit as Alt 2 giving the win to Alt 3)
So at this point Alt 1 has a record of 0-0-2, Alt 2 has 1-0-1 and Alt 3 has 2-0-0. As the qualification matches set you against someone with the same number of wins, I then did:
Main account v Alt 1 (scored an own goal with Alt 1 then quit as Alt 1 giving the win to main account)
Main account v Alt 2 (scored an own goal with Alt 2 then quit as Alt 2 giving the win to main account)
Main account v Alt 3 (scored an own goal with Alt 3 then quit as Alt 3 giving the win to main account)
After these matches my main account had a record of 3-0-0 and if you get 3 wins then you have enough points to qualify for Division 4. I then played 2 more matches (the result doesn't matter, I got hammered in both because my squad was mostly bronze while the people I was up against had very good squads) but after the last 2 qualification matches I was in division 4.
Then it was a case of playing 1 more match in Division 4 and the Trophy popped.