As A Batman main, I can offer you my personal opinion.
Sinestro is tricky if you allow him to control the pace of the match and charge his train freely.
Imho, an important part of this match is the very beginning. When it starts, you can't really go on the offense immediately because Sinestro has a few options from neutral start positions such as his uppercut and jump fear axe. Your best option is to simply back off, activate trait and look for openings (crouch blocking and moving in) since no meter has been gained and he cannot throw out MB Fear Blast which can kill your trait.
Don't allow yourself to be bullied full screen and find every opportunity to close the distance and force him into a corner (where Batman excels). You can throw out Batarangs but trading is useless unless you have the life lead; it's better to keep it cool, look out for MB fear blast and dash in rapidly (releasing bats if available) when you hear / see his impact meteor animation.
Knocking him down is quite important since he has limited wake up options; Arachnid / MB Arachnid are options but easily blocked and punished. You can even bait is wake up by activating bats, dashing in on knock down and dashing out immediately (the similar method to bait / punish a majority of the roster). If he throws out the Arachnid, just release bats and you got yourself a nice combo and possible MB grapple set-ups. If he doesn't, you'll be less than half screen away with trait up and options to get in.
With his trait up, your options are limited but not completely compromised; You can still get in using your trait and he might start using his trait blast just to keep you out and avoid forward momentum. Stay grounded and dash / crouch your way in activating trait (staggered in 1 / 2 bats) to close the gap. Stay out of B1 range; he will be able to make his block string safe with trait and possibly nail you with an overhead / low mix-up. Jumping in is absolutely not an option because his trait will AA into a combo possibly ending with shackles and more (safe) mix-ups.
Hope this info helps, if anyone has anything to add, please do so.
Btw, my secondary is Sinestro.