Here is the full list of all 35 Anomaly Korea achievements.
Complete the campaign on Hardcore difficulty
Destroy 10 towers in 10 seconds
Fully upgrade a unit of each type
Complete all Art Of War Trials
Fool a hacker into attacking a decoy
Complete the campaign
Earn all gold medals in the game
In mission 12, destroy all energy relays without your squad catching fire, on Advanced difficulty or above
In mission 11, destroy every tower in each special zone , on Advanced difficulty or above
Complete mission 10 without activating a single energizer, on Advanced difficulty or above
Earn 500 000 points
Complete mission 9 not triggering any airstrikes, on Advanced difficulty or above
Use a supply unit to spawn 10 abilities
Destroy each tower type at least once
Complete each of the sectors in mission 8 in under 1 min 50 sec, on Advanced difficulty or above
Use every ability 5 times each
Complete mission 7 buying just a single unit, on Advanced difficulty or above
Complete mission 6 destroying all towers, on Advanced difficulty or above
Destroy 1000 towers
Complete mission 5 without losing your Shielder, on Advanced difficulty or above
Collect $10000
Complete mission 4 using only unupgraded tanks, on Advanced difficulty or above
Use Horangi Tank's special attack 10 times
Build a squad of 6 units
Purchase 10 units
Earn 5 gold medals
Complete mission 3 attacking 5 scorchers head-on, on Advanced difficulty or above
Collect $2500
Use abilities 100 times
Complete mission 2 without losing any units, without using Boost, on Advanced difficulty or above
Upgrade a unit
Destroy 100 towers
Complete mission 1 without losing any units, with 4 Boosts remaining, on Advanced difficulty or above
Collect 10 abilities
Destroy 5 towers