The range used to be one number -- a natural twenty.
After the feat, you can crit on two numbers -- a natural 19 or natural 20.
The number of values on the d20 that can threaten a crit is double what it would be without the feat.
You will double the number of critical threats it gets. Is this a one-time monster? Do you expect it to be alive for more than a few rounds? It could be that the feat will make absolutely no difference because it never rolls 19-20, but it could be that you terminate one of your players. Its all theory it this point. Can't say what will happen once initiative is rolled.
A range of "20" gives you a 5% chance of a critical threat. That's what gets doubled, and a 10% chance is given by 19-20.
If something has 18-20 to start with, that's a 15% chance, so it doubles to 30% (heinous!) which is 15-20.
Note that the crit multiplier is not affected by (and does not affect) Improved Critical.
IMHO, a range of 20/x2 isn't worth Improving (unless you get cool special effects on your crits) but anything better is. Your x4 will make your crits devastating and well worth fishing for.
For this particular encounter why? He is already fairly dangerous and after the pc's deal with him they have a murderously deadly tower climb and fight to come .
Also he is a construct not sure if he has feats without looking him up again. If you really need to make him more dangerous give him Max hp or the advanced template or a couple of the shapechangers to back him up