To import your animation into Blender:
Under the Armature tab in the window's right panel, enable the Automatic Bone Orientation option and make sure Force Connect Children is disabled.
Armature
Enabling Automatic Bone Orientation ensures that the bones of your character are aligned correctly in Blender.
If this option is not enabled, your character's bones might appear as in the following image; you should still be able to successfully reorient the animation despite this.
Improperly aligned bones
Next, switch to the Animation tab. On doing this, you should be able to see a preview of your animation in a panel on the left, and a timeline at the bottom. Limit the frame range in the timeline according to the number of frames actually used by your animation.
For example in the image below, since the animation only uses 32 frames, the value of End at the bottom of timeline has been set to 32.
Frame range limited to 32
For the translation of an animation, CRYENGINE requires a root bone that acts as the first bone in the parent-child hierarchy of joints.
Usually the relative position of the character is made the "root", which makes it easier to reorient the model than if, say, the hip joint acted as the root. The root bone is also responsible for translating/rotating the model relative to the world space.
To make the root bone a parent of the hip bone, click on the hip bone and then on the root bone while holding Ctrl. This highlights the two bones; press Ctrl + P, and select the Keep Offset Here option from the pop-up menu to complete the process.
The Keep Offset Here option preserves the offset between the two bones, as opposed to connecting them.
Keep Offset
The hip bone should now be listed as a child of the root in the Outliner.
Although at this point, the animation might be aligned as in the image above, it would have still have the correct orientation when imported into CRYENGINE.
If you'd like the animation to play at a fixed position, you can get rid of the forward motion as follows:
To test the exported animation in CRYENGINE:
With the character selected in the Viewport, assign an animation to it using the Default Animation field in the Properties panel.
You'll notice that when imported, the FBX file generates multiple animation files.
Every time an animation is baked in Blender, a new action sequence is created, which in turn results in a new animation being created in CRYENGINE. If you've eliminated the forward motion of your animation in Blender, for example, you might end up with at least two animation files in CRYENGINE – one with the forward motion, and one without.
If the animation was correctly reoriented in Blender, you should now be able to see it playing in the Y (forward) direction of CRYENGINE's world coordinate system.