My bullet of choice for deer culling and pig eradication when using my .243 Win is the 105gr A-Max.
I?ve felled a suitable amount with that bullet as has my boy and anyone else I lend the .243 to.
Assuming you have a fast enough twist, with the discontinuation of the A-Max, I would recommend the 108gr ELD-Match.
Another I?ve used in guns with slower twist has been the Sierra 85gr HPBT-Game King.