It's the Adobe Camera Raw version you want to update, which may entail upgrading your version of Elements. I don't use Elements so I don't know which version of elements you require for the A77II. Probably the latest available version. All I can advise is to go to your Sony website and do a search.
Sony A7, A850, A77, A700 || Sony>> 70-300G, 28-75 f2.8 SAM, 16-80CZ, 50 f1.4, FE 28-70 OSS, FE 24-70CZ f4 OSS, LA-EA4 || Minolta>> 300 f4 G HS, 200 f2.8 G HS, 100 f2.8 (D) Macro, 50 f1.7, 28 f2.8, 28-135 f4-4.5, 70-210 f4, 500 f8 Reflex, TC x 1.4 HS, TC x 2 HS. || Sigma 21-35 f3.5-4.2. || Tamron SP 24-135.