Hi there. This trophy was a pain to get, very dependent on whether your team is good enough, or the enemy team is bad enough, also reasonably buggy. There have been comments across the internet that if you are the last person to capture the sister and shove her in the vent before the match ends, the trophy will not pop. (Unconfirmed for me, personally.)
First, I would definitely recommend working your way up towards the Choose The Impossible trophy as well. (Rank 40.) This means that you will be able to have a wider range of plasmids and other abilities at your disposal, as well as better weapons and upgrades. I was under rank 40, and had all of the necessary tonics and plasmids.
As you make your way to the sister, I would recommend hacking any vending machines and turrets as possible, that way, when you make your way back across the map, there are more ways for the other team to die. :)
The biggest challenge in this mode, is taking down or getting around, the Big Daddy. It will often be that the Big Daddy and the Little Sister are actually tucked away in a room somewhere, which means that it could be tricky to pick up the sister without getting slaughtered by the nearby Big Daddy.
Using the Houdini plasmid (unlocked at level 16), is an excellent tactic, especially if the sister and daddy are in a wider space. Using the plasmid, wait until any splicers guarding are distracted by your team and snatch the little sister right from under their noses. Next, switch to the Aero Dash (unlocked at rank 4). This enables you to dash away faster than running, and it very useful for making a quick escape.
If possible, get a couple of team members to whittle away the daddy's health whilst the rest of your team takes out enemy players. Once the daddy is down, clear out any players that are still alive or have respawned. Once they're down, pick up the little sister. If you can't communicate with your team, hope that they're decent enough people to guard you as you make your way towards the vent. Once you get there, hold down the button, which will fill a bar, telling you the progress of the sister's escape into the vent. Once the bar is full and the sister has succesfully escaped, you will get a point for your team, and the trophy will pop. Ding!
Note: when you die carrying the sister, the enemy team CANNOT pick her up. This is a godsend. This means that you can potentially whittle away the distance by picking her up and just running towards the vent. When you die again, she gets dropped in that spot. Rinse and repeat, although not recommended. It's tedious and frustrating.
Also note that this could also be a bad thing if you do not know the map, or the sister is dropped by someone else who doesn't know the map, as you/they could start running in a direction where the sister could be dropped and then be harder to get to. DO NOT run into dead ends with the sister!
My brother got lucky as was able to get this on his first try, and I don't know how. I don't know his setup or the plasmids he used, so I'm going to list the plasmids and tonics I would recommend for this trophy. You can have two plasmids and three tonics in your loadout. Since there is a wider range of tonics, I would recommend mixing and matching up the suggested ones and seeing which loadout works best for you.
- Aero Dash (rank 4) - fast dash forwards. Capable of knocking into enemies and dealing them a little bit of damage.
- Houdini (rank 16) - turns invisible. Drains EVE with use, so best paired with Metabolic EVE.
- EVE Saver (rank 7) - reduces the amount of EVE used for plasmids.
- Metabolic EVE (rank 15) - slowly regenerates EVE.
- Speedy Hacker (rank 24) - hack vending machines and turrets faster.
- Leg Up (rank 28) - you can charge jumps, so you can jump higher.
- Fast Feet (rank 30) - faster running and quieter footsteps.
- Death Trap (rank 38) - once dead, your corpse will slowly count down to a timer, and you will explode, dealing damage/killing anyone near your corpse.
- Resurrection (rank 40) - can resurrect with low life after being killed. Watch out for this against the enemy! If they glow blue and you didn't get the kill, it means they will be resurrected. Quickly melee them back into death. :)
Again, these are just suggestions, and I'm sure that you can come up with your own ways of doing this. If I have missed out something important, or you don't like this guide, please comment and I will amend it.
Happy trophy hunting!