If we open our bear's Material, we can see that there is a Material Expression Scalar Parameter that controls the intensity of the eyes glowing with a parameter named Eye Glow Intensity.
You will want to take note of the parameter name that you wish to drive with a Material Curve as that name must be the same as the one used inside the Material to affect it.
The Eye Glow Intensity has a default value of 20 and it is this value that we will drive with our Material Curve to produce a brighter red glow during the animation.
Click image for full view of the Material.
Inside the Animation Editor for our melee attack, we start by clicking the button located in the Curves area, then select Add Variable Curve... and Create Curve.
When prompted to enter a name for the curve, we enter Eye Glow Intensity to match the name of the parameter inside our Material.
This creates the Curve we need, but we must also make sure to identify it as a Material Curve. This is done using through the Anim Curves menu under Window.
In the Anim Curves window, we click the option under Type to make it a Material Curve.
We can now add keys in the curve window (Shift + Left-click) to affect how/when to adjust the parameter's value (we added 4 keys as shown in the video below).