Missable achivements?

[Kowalski]

and could you do any sort of free roam ?

[Xymjak]

Game have not free-roam after credits, you must collect everything after the third boss / before you go to final (game warn you about point of no return).

Missable:
LEAGUE OF SHADOWS - Get a 100 hit combo
Joker Route: www.youtube.com/watch?v=zcFsyargJeg

Bad Case of the Mondays - Defeat Grundy using the Shock Batarang and water
Do Joker before Black Mask.

These two missable only if you specially will not collect a reward for final "quest". And you need complete game 3 times for these, because reward depend on who you select as a last boss:
World's Snazziest Dresser - Obtain all Batsuits attainable through gameplay
The Collector - Find all detective cases and have all pickups and upgrades