Varric likes to talk and likes Hawkes who do too. Solving problems and gaining advantage through diplomacy, outright lies, and even blackmail will impress him, while straightforward violence and thuggery leaves him cold. He also responds well to joking, flirting and sarcasm and to mild greed. Beneath his silver tongue, however, he's a goodhearted person and will appreciate Hawkes who look out for their families and are kind to dwarves.
Finders Keepers: Attempt to trick the guards by the docks with the Star response, "Fire!" (+5)
Note: This will only work if Merrill is not currently in your party as she will unintentionally blow the cover and receives the approval instead of Varric.
Finders Keepers: Upon returning to Martin, refuse to tell him the location of his cargo and then choose the response, "I'll tell you for a price." (+5)
Note: With patch 1.03 or later, you may no longer have the option of demanding for payment. Revealing the location will grant you the approval.
The First Sacrifice: Choose the following dialogue options while speaking with Ghyslain (+5)
Investigate
"Don't you want her back?"
"And you wonder why she's gone."
Get Back to Work: Offer the workers a raise, and upon returning to Hubert choose a Witty response (+5)
Loose Ends: (Athenril path) Give Pryce the goods and then lie to her about it results in (+5)
Plans for the Future Choose any response first and then choose the humorous response for (+10)
An Update: Choose the Charming response, "Let's go get some drinks." and agree to find Bartrand (+25). Alternatively, "You can tell me anything." then agreeing to find Bartrand (+20) or refusing to find him (+5)
Repentance: While speaking with Allure, select "I would never betray my friends.", then choose either of the following dialogue options: "That's a good point." or "Don't listen to her..." for (+5)
To earn rivalry with Varric, choose aggressive responses that glorify violence and combat, and show a lack of interest in his stories, his friendship, and your place in Kirkwall.