For the achievement, you have to complete any 10 Rescue missions.
You really want to have Loki with invisibility. If you do, then there are several low level Rescue missions to choose from:
Grineer:
Mars --
Spear Sector -- one of few low level Rescue missions that is Grineer. Watch out for energy sapping doors!
Corpus:
Venus --
Linea SectorVenus --
V Prime SectorUnfortunately, setting the hostage free does mean you have to run all the way to extraction to count for the achievement. As long as the alarm doesn't go off in the Hostage area before you find the Hostage though, you're good!
However, you don't really have to watch the Hostage on the way out. Run as fast as you can and he usually teleports to you quite often!
I've included my loadouts for speed or invisibility on my Loki Prime below; I personally liked the ability to move very fast just to get to the objectives and extract faster.
My Loki Prime max speed build(Sprint speed 1.96):
*** Spoiler - click to reveal ***(All mods are max rank unless specified)
Aura mod: Sprint Boost -- +10% Sprint Speed
Exilus Mod: Firewalker(5/10 upgraded) -- +13.2% to Bullet Jump +13.2% Aim Glide and Wall Latch, +150% fire damage on Bullet Jump
Madurai polarity slot: Speed Drift -- +12% Sprint Speed +15% Casting Speed
Naramon polarity slot: Maglev -- +30% Slide -30% Friction
Vazarin polarity slots: Narrow Minded(4/10 upgraded) -- +45% Power Duration -30% Power Range
Armored Agility -- +15% Sprint Speed +45% Armor
Regular slots: Cunning Drift -- +12% Slide -30% Friction +15% Power Range
Coaction Drift -- +15% Aura Strength +15% Aura Effectiveness
Rush -- +30% Sprint Speed
Continuity -- +30% Power Duration
My Loki Prime invisibility build(203% Power Duration):
*** Spoiler - click to reveal ***(All mods are max rank unless specified)
Aura mod: Energy Siphon -- Warframe energy regenerates +0.6 Power Rate
Exilus Mod: Speed Drift -- +12% Sprint Speed +15% Casting Speed
Madurai polarity slot: Continuity -- +30% Power Duration
Naramon polarity slot: Constitution -- +40% Faster Knockdown Recovery +28% Power Duration
Vazarin polarity slots: Narrow Minded(4/10 upgraded) -- +45% Power Duration -30% Power Range
Redirection -- +440% Shield Capacity
Regular slots: Overextended -- +90% Power Range -60% Power Strength
Streamline -- +30% Power Efficiency
Rush -- +30% Sprint Speed
Hushed Invisibility -- Loki Invisibility Augment - Weapon noise is reduced by 100% while invisible