These are just guesses, but every three or so people I defeated on Survival got me the golden card for one character that I haven't unlocked yet at that point. (But my opposition was mainly characters that I haven't unlocked yet, and the RNG decided to sic Lu Bu on me early...)
I've also gotten the golden card for characters for having a total of 4000 KOs (this was on Easy). The bulk of my golden cards were obtained from grinding for bonds, and the only gold card that I got from Story Mode were the three main characters and Daqiao (the last one was because I spammed the EX attack repeatedly, while the main characters... if you play with the recommended team every time, there is no way you can't get your 4000).
so far i only know 3 confirmed ways for certain golden cards. S-ranking a character's proficiency, winning up to 100 kills in survival, and fighting the character in duel mode. (not survival) but people like rachel and muneshige i have done those things for, but don't have their golden cards.
I can confirm S-ranking proficiency unlocks cards for some (and even on Easy, you can play the Yiling mission and stall until your kill count is north of 3500 to get that...)
As for unlocking golden cards in duel (or survival) mode, I think you only get one member at random guaranteed for every team of three on Easy. I've tried a few times, and I only got the card for the last person defeated if I didn't have their card already. There was one occasion where I got two cards, but I think it was from finishing one of them with a Musou attack.