What do I put for "Date Acquired" for my ESPP if my 1099-B form says "Various"?

You can enter "various". Make sure you select Under the Select the information type you see in Box 1b, there are two options. Select the second option, Something other than a date. Select Various (or more than one date) and continue with the onscreen interview until complete. 

Regarding your ESPP, since the gain on that stock sale was included as income on your W-2, to avoid double taxation:

• You will need to change the stock basis on the date of the sale, to the price on the date of sale.  
• The result is zero gain or a minor loss due to brokers commission/fees.  
• The IRS will expect to see that information on your tax return.  

To enter your 1099-B form, see Where do I enter a 1099-B?

For additional information, see the TurboTax article: Non-Qualified Stock Options.