You just have to wager a weapon that satisfies the amount they want and beat the previous floor boss. However to enter the 10th floor you have to wager an item worth 102400 Gald and have beaten all the previous floor bosses and the 3 Great dragons at each of the Valkynes.

You just have to dualize equipment worth increasingly more money. I don't know the exact amount for 8th and 9th, but apart from sidequest 64, you also need something that you can sell for over 204800 gald. So you just need to get to dualizing.

I just use a joke weapon with perilous shard for 200% resell value as my item of choice and if i die i reset to reload so i won't lose it.