This one is a bit challenging as you kind of have to go out of your way to do it and it means you're going to be a bit of a dick throughout the game.
The people who you will contribute to their demise in order are: Mary, Colbert, Quince, O'Leary and Sonia.
So try not to form any attachment to them...
Mary: 1) When first interrogating Mary at the diner the conversation of future jobs will come up. Chose "stay to work at the gym" 2) After opening the safe in Dunn's office don't tell Sonia about Mary's relationship with Dunn. (Mary plays an important role in the story and directly effects all the endings on whether she is alive or dead)
Colbert: Regardless of what interactions you make with him before sneaking into O'Leary's office all you have to do is rat out Colbert that he was cheating with O'Leary's wife. (stops you from getting the Niagara falls achievement)
Quince: When playing poker with Cassidy, towards the end you have the option to use your cat sense on Quince. Use it to rat out that he was cheating the entire time. This is the only dialogue option with quince that makes you an active contributor to his death. (stops you from getting the Zero Tolerance achievement)
O'Leary: After pier 36 you get to talk with both Yale and Stone. Tell Yale to not take the drugs and Stone to not hold back and throw the fight. a surprisingly easy one to miss.
Sonia: Fail the final QTE to push the gun away after exposing Tim and refusing to sympathise with him.
Note that Jimmy (dog that O'Leary shoots in his office), Randal Leigh (Anteater), and Craig Spannow (ex-Baseball player monkey) are all unavoidable deaths that happen regardless of options you choose and are not counted. If you try to save Jimmy, Blacksad will be killed. Randal will fall regardless of whether you try and help him and Craig will die despite your efforts to save him.
All other deaths that Blacksad can contribute to will fail the game, not counting towards the achievement.