TCG Eloc :
I usually get 20-25 on ultra and 30-40 on standard and it is on 1920 by 1080.
Then I don't think anything is really wrong. It's a really demanding game, and one of the games for which people spend a lot of money on a gaming system.
I'm not quite sure why you expected to get above 25FPS on Ultra settings at 1080p anyway with a mid-range CPU and mid-range graphics card.
*Like any game, don't just crank the graphics quality. Rather, decide on your frame rate target (i.e. 40FPS average with VSYNC OFF) and adjust the settings to achieve that.
It's possible 1600x900 may make more sense but you can decide. It depends a lot on how large the HUD/text elements are for the game as lower resolution can make these blurry. I don't own ARMA III so have never experimented.
There's an optimal combination of the settings. Some people prefer more anti-aliasing, some prefer a higher frame rate etc. Often there are settings like SHADOWS, or Depth of Field which are far more demanding than other settings for the amount of obvious visual benefit they provide so those are ideal to turn down or even disable.