When you return to Detroit during the riots and meet with David Sarif in your apartment, he will give you a pass to enter room 2005 at the Detroit Convention Centre, where Bill Taggart is currently giving a speech.
Save your game BEFORE entering the convention room, entering the room will trigger the conversation with Taggart, so saving the game allows you to quickly restore if you turn him against you.
You must engage him within the convention room, and not backstage, and it is worth noting that you can miss this achievement if it takes you too long to get to room 2005.
To get this achievement you do not need to have the C.A.S.I.E augmentation, however it will assist with reading his personality. Without the C.A.S.I.E augmentation it is worthwhile keeping in mind that Taggart is a prima-donna, so personal attacks will undermine his confidence in replying, setting you up for your next reply.
Use the Confront response against Taggart as your initial response to knock him off guard, and then follow-through with the rest of the conversation.
Remember the following when selecting your follow-up answers:
When Bill Taggart has no information to exploit, he will base his arguments on his personal ideals
You can threaten to give the recording to the reporter or press to test its genuine status, and that will pressure Taggert into giving you what you want
It is revealed during the conversation (if you select the correct options) that Taggart's wife, was killed while attempting to assist an augmentation rejection patient. Humanity First was started by Bill to "remedy" that problem and you should use this knowledge against him when possible
Take note that due to a certain element of randomness a 'definitive' list of options to select cannot be guaranteed when paying attention to the C.A.S.I.E augmentation, however by making your choices based on his psychological profile you can nearly guarantee success.
Such a path involves the following choices: Confront, Discredit, Redirect, Redirect.
He will then fold in public, granting you the achievement, and invite you backstage to give you the information you require regarding Isaiah Sandoval's whereabouts.