Dumping every idea I can think of.
(I'm not very good at naming, so feel free to change it up!)
* Use Trojan hack -- Trojan Attack
* Use brute force hack -- Brute Force Attack
* Perform 10 commands in a single terminal -- Maximum Efficiency
* Perform 3 manual commands with success in a single machine -- Obtaining Deep Network Data
* Obtain an unexpired data core -- Robot Brain
* Recall a squad -- Going back home
* Attack x number of annoying recyclers -- Stop touching my stuff!
* Destroy a behemoth -- Giant Slayer
* Assimilate a behemoth -- Pet GIANT (has anyone done that already?)
* Assimilate a prototype hostile enemy -- Prototype Assimilated
* Reprogram a programmer -- Hack the Hacker
* Intercept x number of haulers in a single run/floor -- Treasure Hunter
* Destroy an army of assemblies before the dispatcher arrives -- Already Took Care of 'Em
* Destroy an enemy by ramming -- Fist Fight
* Destroy an imp before it sabotages -- Oh No You Don't!
* Sabotage an enemy -- Sabotager
* Destroy an unaware using guided weapon (pun intended) -- Target: Unaware
* Achieve kill streak of 20 -- Killing Spree
* Attack an enemy using melee weapon with at least 4 momentum -- Deadly Strike
* Attack with a high attack speed (less than 100 time unit per attack?) -- Pew pew pew pew pew!
* Achieve 100% critical hit chance (through utilities and weapon) -- 100% Chance of Destruction
* Fire with at least x number of overloaded weapons -- Eat This!
* Travel with x number of overloaded propulsions -- VROOM VROOOOOM!!
* Overload x number of power equipments -- Power Overwheming
* Unleash 3 follow-up melee attacks at once -- Melee Mastery
* Destroy 2 robots in one melee attack -- Deadly Assassin
* Use melee weapon to dig through x number of wall tiles -- Part-Time Excavator
* Increase sight range to over 20 -- Vision 20/5
* Absorb at least x damage using force field/mantle/etc. in a single turn -- Can't Touch This
* Jam at least 10 distress signals in a row -- Static Signal
* Extract x number of traps -- Trap Master
* Gain at least 30% evasion bonus through items -- Dodger
* Get to the stairs with less than 10% of core health -- Well, that was close
* Go through and survive 2 garrison areas in a single floor -- Garrison Survivor
* Go through and survive 2 waste areas in a single floor -- Wasteland Survivor
* Complete a floor while being overweight the whole time -- Overweight
* Achieve a high exploration rate (at least 60%?) -- Cogmind, the Explorer
* Visit 10 branch areas in a single run -- Branching Out
* Obtain a total part rating of x -- Deadly Loadout
* Fly over x number of (hostile?) robots -- Whoosh!
* Have at least 50% of corruption -- Highly Corrupted
* Reduce corruption to 0% using items -- Self-Cleaning Bot
* Evade a faulty item's negative effect -- Safe!
* Insert an item, process, and obtain matter in a single Recycling machine -- Part-time Recycler
* Store at least 1000 matter -- Matter Hogger
* Store at least 1000 energy -- Energy Lover
* Cause havoc at Zion -- Zion Invasion
* Abuse the fabricating machine until it shuts down -- Fab to the Max!
* Collect x number of lores -- Lore Collector
* Discover x number of different items -- Item Collector
* Collect 3 analysis of different robots in a single run -- Robot Analyzer
* Identify a prototype using items or by using a Scanalyzer/repair station -- Safety First
* Win without destroying a single robot --
* Beat the game in [insert challenge mode]
* Die at the scrapyard -- Don't Want to Move On
* Kill yourself using explosive weapon -- Suicide Bomb