This is more of a warning
than a full solution. -- The game does not appear to record your progress in Expedition Mode unless you are connected to the Square Enix servers. This makes this achievement Online Required
for this achievement you will need to earn gold on one level in Score Attack. if you have it unlocked, the Chamber of Exorcism is very easy, only requiring 5000 points for gold, and giving you plenty of time to earn over 10,000 just from the time bonus. you won't need to use any cards. (credit: https://www.trueachievements.com/LuckyConquerer2.htm
there is a guide at the following achievement's solution showing how to solve the puzzle in case it trips you up. once you get that down, it should only take about a minute or so to complete the level, making it also a good level to earn that achievement, as you can earn gold on the same level 10 times.
NOTE: i am not 100% certain that you can simply play the same level 10 times. me and another user had gold on less than 10 different levels, so it seems to count them more than once, but maybe not always. i am thinking maybe only if you beat your high score, will it record it as a new gold medal. either way it's better to go for all the bronzes first, you will probably get gold first try, or after repeating a level once or twice.