This achievement is stackable with other difficulties.
I would recommend playing through on Normal or Easy first (the game is pretty easy even on Normal) to unlock the majority of the character and combat upgrades. Make sure to focus on Character upgrades to get maximum durations for special abilities and maximum health/regen.
On Hard, enemies take more damage to kill and inflict quite a bit more damage. If you've already played through once, not only will you have most of the upgrades but you will know the boss patterns and what is expected in each level.
Some of the most difficult parts are defending civilians/scientists while they work on something. The Y+B move you can unlock is great in these cases as it hits a wide area and stuns the enemies before they can damage the civilians. Along with that, the airborne Y stomp hits a wide area and stuns enemies. Since they are timed and you don't have to beat all the enemies, simply jumping in place and slamming down with Y repeatedly can usually buy enough time. Don't forget to use Rage or Accelerated Vision if they are available.
While you playthrough on Hard, focus on doing a lot of different combos and picking up spider emblems. This will allow you to get platinum medals in both of those categories (you probably won't get Platinum in time unless you really rush it) so you will be 2/3 of the way toward getting the Platinum medal for each overall level.