Once you have met the Chamber 3 shortcut requirements, you will find the Tailor NPC under the elevator in the starting room on chamber 4.
Give him these items in order to access the Chamber 4 shortcut (must be given in this order, apart from the Master Round which can be given at any time):
- 4 pieces of junk (shoot and break chests to acquire junk - this is a random drop)
- 5 keys and 240 shells
- 20 hegemony credits
- Master Round 3 (earned by beating the 3rd chamber boss flawlessly)
Once you turn in all requirements, the achievement will unlock and the Tailor will request to speak with you in the Breach. Speak with him and receive a new item or gun.