Although the first guide provided valueable information on the community challenge to select, I thought it was worth adding some details with regards to execution.
This below is how I got the achievement for beating Fel before her combat phase. Please note that I have not beaten Deadalus before his combat phase using this guide.
Access the Community Challenge section and search for "StoreSurplusRates" --> Start run
Champion Upgrade: Glutton
Artifact: Skip
Level 1 Fight
Turn on the trial
Put the champion on the bottom floor so that you are able to get the bonus gold in the second round on the middle floor
Rewards: Only pick Morselmaster, skip the other cards
Level 2
Take the left path
Pick up the gold
Apply Emberstone to a Shadesplitter card
Reroll
Apply Emberstone and Holdover to another Shadesplitter card
Remove a card from your deck (e.g. Restore)
Level 2 Fight
Turn on the trial
Put your Champion on the bottom floor
Put your Morselmaster behind your Champion
Add Morsels to the bottom floor to feed to your Champion (twice as powered by the Morselmaster)
Rewards: Skip all cards
Level 3
Take the right path
Add a Strengthstone to your Morselmaster
Remove a card from your deck (Restore e.g.)
Pick a second Morselmaster from the banner
Skip the event
Level 3 Fight
Put your Champion on the middle floor, put your Morselmaster behind your Champion and add Morsels to the floor as before
Put your second Morselmaster on the top floor and use your remaining cards as required
Rewards: Skip the first card, pick the Overgorger
Select the capacity upgrade (you can alternatively select the additional card draw)
Level 4
Take the right path
In the shop, apply Emberstone and Holdover to a Shadesplitter card
Skip the card as offered by the banner
Pick the Glutton upgrade for your Champion
Level 4 Fight
Put your Champion on the middle floor, put your Morselmaster behind your Champion and add Morsels to the floor as before
Put your Overgorger on the top floor, put your second Morselmaster behind him (this might not be possible right away depending on the card draw) and keep adding Morsels
Rewards: Pick Shroud Mitosis
Level 5
Take the right path
You can duplicate Shroud Mitosis, if you want
Remove two cards such Restore and Train Steward
Level 5 Fight
Put your Champion on the middle floor, put your Morselmaster behind your Champion and add Morsels to the floor as before
Put your Overgorger on the top floor, put your second Morselmaster behind him (this might not be possible right away depending on the card draw) and keep adding Morsels
Use Shroud Mitosis to create more Morsels
Rewards: Skip all cards
Level 6
Take the left path
Pick up the gold
Buy Fossilized Fangs from the Merchant of Trinkets; use your remaining money to get rid of cards you do not need
Level 6 Fight
Put your Champion on the bottom floor, put your Morselmaster behind your Champion and add Morsels to the floor as before
Put your Overgorger on the middle floor, put your second Morselmaster behind him (this might not be possible right away depending on the card draw) and keep adding Morsels
Use Shroud Mitosis to create more Morsels