Comebacks are a new feature and are represented by a meter that's built up by your opponent's insults. The stronger insults they throw, the more it build ups your meter. The meter fills in 3 bars with stronger Comebacks for levels 2 and 3. For this achievement your best bet is to use them early and often. As soon as one bar is filled and your insult is finished, hit "y" to tack one on at the end. Do this three times in one fight and the achievement should be yours. Comebacks should not be confused with the standard exclamations that can appear under the LB or RB buttons and were included in the first Oh...Sir game, those exclamations don't count.
This achievement is a bit of skill mixed with luck. Sometimes you'll be a sliver from level 1 being filled and your opponent will hit you with an insult that builds it right to level 2. You can try using up and/but words, but you also want to be wary of making your combos too strong as you can easily finish most opponents without getting past 1 or 2 comebacks. Learning how to string them along with basic insults is beneficial as there are a lot of Golden Parrot Trophies in career mode that require using 3 Comebacks and achievements tied to them.