This is a lot easier than it sounds.
During the campaign, complete every companion quest as this normally improves relations and then Make sure to complete all side quests given by each faction leader.
There are five factions:
Coin Guard (Arguably the hardest to get trust from)
Theleme (Medium, can easily loose points by mistreating missionaries)
Bridge Alliance (Hardest to gain trust with).
What I had when the quest to unite the factions activated:
Bridge Alliance - Friendly
Theleme - Friendly
Coin Guard - Nice
Nauts - Friendly
Natives - Friendly
The Coin Guard will be okay at Nice as long as you follow Kurt's suggestions for the new leader of the Guard and you can even kill Egon. Quests
Missing In Action (Kurt)
Amongst the Ghosts (Kurt)
Settling scores (Kurt)
The Man with the Silver Coin
Champion of the Arena
The Natives are simple, just respect their customs and make sure they are accepted by the rest of the world. Getting the Merchant to run his business in New Serene also adds alot of respect points. Quests
Find Queen Bladnid (Siora)
Promises set in Stone (Siora)
The Queen's Farewell (Siora)
The Blood Price
An Aspiring Merchant
A Peculiar Alliance
Camp of Ordo Luminis
The Nauts are also very easy, just dont kill any uneccessailly and dont raid or get caught inside one of their storage facilities or dockyards. Do all side quests for them before leaving old serene too, find the missing Naut for Vasco. Quests
A Name for a family (Vasco)
Family Reunion (Vasco)
Forever a Naut (Vasco)
The Admiral's Secret Service
The Spy from Theleme
The Enemy Within
Theleme is simple, but you can loose points REALLY quickly by mistreating the missionaries on Native maps. Doing all of Petrus' quests boosts it to Nice. Then make sure you get them to reveal the truth about themselves to other factions when talking to mother superior during their side quests.
Help them first when dealing with the aninal attacks during the main questline. This maxes out the friendly status. Quests
The vices of the Mother Cardinal (Petrus)
Dangerous Bets (Petrus)
The Sins of Father Petrus (Petrus)
Trouble in Eden
In the Footsteps of Saint Matheus
Saint and Wild
The Attack on San Matheus (Main Questline)
Bridge Alliance - During their side quests, take Doctor Asili to court and get all witness' and evidence against him. then watch him as he gets killed. You seem to get more points by taking Aphra with you to watch it.
Make sure you follow the side quests acting in their best interests.
Doing Aphra's side quests without killing their researchers also helps dramatically.Quests
Islander Knowledge (Aphra)
The Cave of Knowledge (Aphra)
The Linking Ritual (Aphra)
Attacks on Caravans
At the Heart of the Rebellion
Doctor Asili's Experimente (MUST ACCEPT SURRENDER)
The Attack on Hikmet (Main Questline)
It's worth noting that because The Coin Guard were nice, I ended up with this end trophy
To get the gold, I'd have had to have them at Friendly also.