I strongly recommend that you acquaint yourself with the hints contained below still before you start playing. This will let you learn about a few important dependencies, which will make starting off easier.
1) Although Arkham Asylum is a prequel in relation to the previous installments, from the storyline's point of view, right at the Beginning, Batman can pull off many movements (e.g. attacking armored enemies), and has gadgets (e.g. the Bat Claw or the Explosive Gel) from the very beginning. In the case of the Arkham Asylum and Arkham City these became available only after some time into the game. As a result, it is worthwhile to spend some time to get acquainted with the information in Batman's menu, and more precisely with the descriptions of all the basic movements (the Main Controls tab). The game is trying to describe the attacks and gadgets that you use for the first time, on a regular basis. Still, knowing them beforehand, may speed up the completion of the early stages of the game, or make it easier to fight at the initial stages.
2) One of the innovations in Arkham Origins is the detailed mission rating, displayed by the game after each fight (i.e. the number attacks in a chain, variety of blows, etc.). It is a good idea to read those each time in order to improve on own skills and, which follows, to gain more experience points.
3) In Arkham Origins you can return to the Batcave, which of course performs the role of the Bat's headquarters. I recommend that you talk to Alfred on a regular basis (sometimes it is rewarded with experience points), as well as to unlock the optional challenges throughout the main plot, to the extent it is possible.
4) While exploring Arkham, do not ignore the information on the crimes under way. Dealing with bandits is not too demanding, most of the times, and you will be rewarded, in exchange, not only with additional points for defeating your enemies, but also with a special bonus to your experience (most of the times, this is several thousand points).
5) The exploration of the game world can be made more efficient in two different ways. In Arkham Origins Batman has access to the upgrade to his hook launcher from the very beginning. Therefore, it would be a good idea to catapult yourself in which Batman attaches his hook. Apart from that, I recommend that you unlock al fast-travel points (Batwing drop points) as soon as this becomes a possibility (you need to sabotage Enigma's communication towers).