To pop this one, you need to make certain selections over the course of the meeting at Café Alps with Oda during Chapter 5.
For starters, you’ll need to select the table near the back. Oda will mention that it’s the perfect place to talk business. Next, you’ll want to take the nearest seat. Oda is impressed with you placing yourself at the foot of the table and remarks to keep applying your experience as a lower-level yakuza to the client. The waiter will show up a moment later, and you should tell him you want nothing. Again, Oda is impressed and remarks something about “smacking the rude out of you” if you’d chosen to order before the arrival of your client.
Your client will enter. Be prepared for a quick time event. If you pull it off, Kiryu will (clumsily) present his business card to the client. The speed with which you press the correct button will determine how clumsy Kiryu is with the card. Oda makes an observation about the importance of business cards, and the client reassures you. Finish your conversation with the client, and the achievement is yours.