First step: beat the game on SURVIVAL, don't play on Casual on your first run, it's a waste of time. And don't play Nightmare, it's also a waste of time if you're planning on beating the game on AKUMU.
Recently I finished this mode (no upgrades, using almost all the keys I found on the way) and here are a few tips to complete it:
1- You can get stealth kills, actually, they aren't that hard to perform. If you have been doing it the way the game recomends you to do it, then you will not find any problem with it (always be behind your enemies, crawling, with your light off). The only difference with other difficulties is that enemies detection field is a little bit more wider and realistic.
2- Taking into consideration the previous point I really encourage going for stealth kills whenever you can. It can take longer to do but in the long run it will save lots of ammunitions that you will need for enemies that are impossible to kill stealthily. And even for those kind of enemies there are "low-cost" tactics to kill them: exploding traps, burning them with your matches or going for hit-n-run (and shoot) tactics. Make good use of the enviroment, it might be hostile for you, but it can be hostile for your enemies if you play well your cards ;)
3- Be careful when getting close to enemies lying on the floor, they have the annoying tendency to jump with an attack, not mentioning that they recover faster than in Survival.
4- Be careful with proximity traps, they're waaaaay harder to deactivate in AKUMU mode. If you are close to a save room or you're at the beginning of a checkpoint, you can try to deactivate it and get its components for your crossbow. In case you aren't close to a checkpoint (and had gone through a hard section) I don't advise trying to deactivate them, wait for a checkpoint to give it a try.
5- There are more traps than in Survival, but it also means more pieces for bolts, which is good news.
6- In this mode checkpoints works a little bit different, in some cases they play at your advantage and other times... well, you will see it.
7- Make good use of your crossbow bolts. Don't create new ones unless you have none and need a specific one for a crowd or a boss. If possible, try to get new bolts from the enviroment or the lockers in the save room.
8- Lightning bolts are great for crowds, freeze are good to slow down bosses and flash are a good option when you need to run away from crowds of enemies (or getting a free stealth kill).
9- In case you don't mind expending a little bit of extra money (real) I would recommend "The Fighting Chance pack" DLC, for the incendiary bolts, since they are actually the best bolts for crowd-control (better say, crowd-annihilation). The double-barrel is also included in this DLC and is a very good weapon to start with (until you upgrade the shotgun you find at chapter 3).
10- Although I completed the game without upgrades, I really recommend you to USE ALL THE GEL YOU CAN and upgrade your stamina, critical hits and stock. If it weren't because I wanted to skip one full playthrough on getting the "It Is What It Is" I would have upgraded right at the start. Don't upgrade anything related to your health and syringes, it's completely useless.
TA user 'Sepharim17' wrote a solution for the x360 version of this game which includes a playlist of how he beated the game on AKUMU without upgrades and keys. As I said, I don't recommend doing this, still this playlist can give you a good set of guidelines of how to beat certain sections.
One last thing I want to add: Once you finish AKUMU (or Hard difficulty) you will unlock the brass knuckles, which are a beast in new game+ and help a lot to get the 5 hours playthrough achievement (I would recomend trying on easy for this one,... unless you feel brave enough to do it again in AKUMU).