The bonus “Greater Variety” must be earned in order for this achievement to pop. Just perform actions until the bonus pops. Note that it’s a bit easier if you have poison or the gun unlocked. Here’s a possible list of bonuses to go through (much easier done if you are boosting):
1: First Blood (Can be done with the following three bonuses, or separately. Just be the first one to kill in the game session)
2: Hidden Kill (Hide in a haystack and kill your target)
3: Focus (Can be done with hidden kill, ensure the meter around the button is completely full and flashing)
4: Incognito (Can also be done with hidden kill, just hide until your kill meter is full (“incognito”) and then kill your enemy.
5: Ledge Kill (Hang on the side of a building with your target above you, and kill them while they are above you on the roof)
6: Acrobatic Kill (Get on any of the narrow walkways connecting between buildings and kill your target from there when they come within range)
7: Gun Kill (You must be level 17 to have the gun, simply kill your target with the gun to get this bonus)
8: Silent (Kill your enemy when your kill meter displays “silent”)
9: Discreet (Kill your enemy when your kill meter displays “discreet”)
10: Reckless (Kill your enemy when your kill meter displays “reckless”)
(Greater Variety should unlock, also unlocking the achievement. )
This is just one of many possible combinations to unlock the “Greater Variety” bonus. Many other bonuses can be used to get to this, just ensure that there are ten different bonuses in total. Also ensure that you are playing any game type on the map “Firenze”.
NOTE that this achievement can also be obtained in Training Ground. A big thanks to PS3T user 'Moving On' for the following explanation:
Okay, I just finished my extensive experimenting and you indeed can get Greater Variety on the Training Ground. There's a few key things you have to keep in mind.
Aerial Kill does not count towards variety. I was pretty sure it didn't, but I made sure and checked it this morning. The Aerial Kill is just another way to say "Kill" and it doesn't count as a bonus.
Variety does not count towards variety. Again, I was pretty sure it didn't, but I made sure and checked this, too. So upon getting "Variety", your bonus count doesn't go up to 6, it stays at 5. Greater Variety doesn't count either, so after getting that bonus, you're at 10 bonuses instead of 11.
Streak bonuses do count towards variety. I'm actually not sure if this was the case in Brotherhood, but I had noticed it a couple of times in Revelations over the past few months.
Animus Hack does count towards variety. Interestingly enough, this is a bonus separate from the Streak bonus and there's the key to getting Greater Variety on the Training Ground: only by using the Animus Hack streak can you actually get those 10 bonuses. Keep in mind that the bonus "Animus Hack" only shows up when you actually kill a pursuer (impossible on Training Ground) or your true target. Killing a non-target NPC will not give you points or the bonus.
So here's the list you need to get the Greater Variety bonus on the Training Ground.
10. Animus Hack
I've read somewhere else that it should be possible to also get the Execution bonus if you bring the Hidden Gun and start a chase with your NPC target. I tried that, but couldn't get the bonus and in general, it sounds like too much of a hassle. The list above is enough to get Greater Variety (remember to pick Florence as your map, though) if you use an ability set that has Poison and one of the two Animus kill streaks (preferably the 9 kill version, so even kills below Silent count).
Note: This can be boosted in a private match.