I've started a new game and got into a battle with some darklings. Used a bow attack and I had a significant delay before attack. (probably 2-3 seconds). Looked at the debug.err file and didn't give any information beyond I used bow attack.

Debug Message:  NOTE: The extra tiles don't appear to be in MapData at this point.
Debug Message:  Map Generation Complete Debug Message:  InitMapGfx Started...
Debug Message:  InitMapGfx finished. Debug Message:  Creating tactical terrain gfx...
Debug Message:  TacticalMapViewWindow::FinishInitMapGfx started.
Debug Message:  WARNING: CResourceManager::GetEffect could not find file: gfx/fx/fxo/post_hdr_shadow.fxo
Debug Message:  CResourceManager::GetEffect found source file for effect: C:\Program Files (x86)\Steam\steamapps\common\FE Legendary Heroes\Gfx\fx\post_hdr_shadow.fx (This will be compiled at run-time and used)
Debug Message:  WARNING: CResourceManager::GetEffect could not find file: gfx/fx/fxo/post_camerashake.fxo
Debug Message:  CResourceManager::GetEffect found source file for effect: C:\Program Files (x86)\Steam\steamapps\common\FE Legendary Heroes\Gfx\fx\post_cameraShake.fx (This will be compiled at run-time and used)
Debug Message:  TacticalMapViewWindow::FinishInitMapGfx finished.
Debug Message:  Tactical Spell cast: BowAttack_Basic at 16, 14 by Lady Irane (unitID 0).
Debug Message:  Tactical Spell cast: DoubleStrike at 15, 15 by Spearmen (unitID 498).
Debug Message:  Tactical Spell cast: BowAttack_Basic at 16, 14 by Lady Irane (unitID 0).

The bolded is the attack that delayed. I'll post the full debug.err file after I finish the playing for the hour or so.

(I'm running an unmodded game with all the DLC available).

Edit: Happened again against another darkling (new tactical battle, first bow attack). It is early game I've got the crude shortbow and I just attacked a party of darklings and a group of darklings.

Edit: https://dl.dropboxusercontent.com/u/75549875/Fallen%20Enchantress/debug/June25/debug.err (debug.err file for that particular game session) It only occurred with the basic bow attack) I fought darklings with the Ignys shortbow and didn't encounter the problem.