Method 1:
Create an extra calculated column which will just store the first letter of the Title column.
LEFT([Title],1)
Map the crawled property of this new column to any existing RefinableString managed property and use it as refiner in the Search results page
Method 2:
Create a new custom refinement template by copying and editing the Filter_default template ,which will display only the first letter of the property.
1.Get the first character.
var refChar=refinementName.charAt(0);
2.Change the code to display refChar instead of refinementName .
<div id='RefinementName' class='_#= nameClass =#_'> _#= $htmlEncode(refChar) =#_ </div>
Add a refiner for Title property and use this refinement template