Gears of War

Single Player: Before you go out to fight him pick up the Torque Bow and either the Sniper or Lancer and make sure you have full grenades.

To start off take cover behind the cover right in front of you, fire a Torque shot into him and it will dissipate his kryll shield, then switch to your lancer/ sniper and let loose on him until his kryll shield comes back. Then rinse and repeat, if you run out of torque shots use your grenades and when he gets up to the cover your at, book it to the other side if it comes to that.

Co-op: Pretty much the same thing except each person can take their weapon of choice. One with torque, other with sniper/lancer, it is a lot easier this way, but if you cant find a partner just follow the above solution and you should do fine.

There is a way to kill him in co-op on Insane in about 30 seconds without cheating.

Just be sure before the fight that both players have Torque Bow. At the beginning of the fight cover and shoot RAAM with all shots from Torque Bow. About 30 seconds of shooting just from Bow and RAAM is going down. Just look out when he's shooting.

This is easiest on co-op, but can still be done on your own.

The strategy is to remove the Kryll shield from General Raam, so you can shoot his head. This means you need to take the torque bow and longshot (it can be done with lancer), as well as grenades. Then, as he moves towards you, fire an arrow at him, and once the Kryll are scattered, aim for his head and get as many shots in as possible. Repeat this for as long as you can.

After a while, he will come very close to your position {if you are playing on casual you could have already killed him}, so then you need to roadie run past him and take cover further down the train. You must make sure that you stay in the light areas to avoid being killed, and then simply repeat the above tactic until he goes down. (You may need to run past him again)

I tried the longshot method and the torque bow method and having to run back and forth, just wasn't working for me.

So...I stood my ground at the starting point of the fight, I drilled a few head shots into him with the longshot and when he got close to me, (other side of the barricade), I switched to the lancer and unloaded on him with blind fire until he went down (he never crossed the barricade)

I don't know if I got lucky or what, but it sure worked and a lot faster than the other methods (for me). This strategy was used in single player.

Th easiest way to do this is in Co-op. Find someone who is willing to help you. When you start the level, DO NOT GO OUT THE DOOR. Grab the weapons in the room. Player 1 gets the Torque Bow, Player 2 gets the Longshot. As soon as you go out the door, take cover! This is vital if you want to defeat him. And duck avery time he starts shooting at you. Player 1 should shoot him with the Torque Bow as much as he can. Every time the Krill leave RAAM, Player 2 should shoot as many headshots as he can. Eventually, with perfect timing, you will defeat him before he reaches you.

the way i got this was using the torque bow,lancer,and grenades, best way to do it is just stay behind the first cover, load out all of ur torque bow into raam untill u run out then switch to the lancer and then throw out all of ur grenades at him then start full out shooting at his head with the lancer,trust me this was a pain in the ass for me trying to use the torque bow then switching to the sniper back and forth and that was way to time consuming so it took me about 6-7 till i finally got pissed off and used the torque bow and lancer and grenades with the method that i just typed in

For those looking to get this AND the Insane playthrough
RAAM is by far the most difficult part of the Insane solo playthru, mostly because when you have to move to new cover (and you will) his chaingun, his shield Kryll, or just the sky Kryll, will often cut you down. His shield Kryll, when attacking, can get to you in the light; you need to be in cover when they're coming at you. The sky Kryll can only get to you in the dark. It is extremely hard to get to new, effective cover and get a couple of shots in before you have to move again. After hours of trying, I couldn't finish this solo playthrough, simply because of the RAAM battle.

Damaging RAAM:
On Insane, he can cut you down very quickly. There isn't much time to aim, so have your screen roughly centred on him before you poke your head up to aim. For the torque bow, start charging it for a second or two with the fire trigger before popping up with the aim trigger, then nail him with it (preferably his face/neck).
Explosive weapons are needed to make his Kryll shield go down, at which point he's vulnerable to damage. When shielded, he doesn't take much damage, if any.
Torque/sniper and torque/lancer (& nades) seem to be good bets, and they're all available in the last room. Active reloads and moderately accurate head/neck shots for the sniper or lancer are important, because there is time pressure here. Get as many good shots in as possible before having to move cover.
Lancer/sniper is also good - it's nice to have a decent non-sniper weapon to blindfire with when RAAM is close to you - but you'll have to wait alot for him to send away his Kryll shield. Only explosives can make it go away, and you'll have no torque bow & only 4 nades.
The glitch where he gets stuck on a block still occasionally works (as of Jan 2016!), and isn't likely to be fixed I suppose lol - gives a good opportunity to "take it slow" and pump some damage into him.

If you can move to new cover without getting cut down, that's probably half the battle there, because then you can buy yourself more time. On the Hardcore version, moving cover is nowhere near as...fatal.
Note: the troika at the far end, if you get there, is vulnerable to Kryll attack.
Note (again): co-op is easier, because Dom can actually be useful then. Even the troika might be worth a (quick!) spin if your buddy has him distracted.

This worked for me on Hardened. Bring the Lancer and the Torque Bow and Frag Grenades. Max Inventory for all. When you start, stay behind back wall and just keep hitting him with the bow and switch to lancer when the Kryll fly off of him. When he starts approaching you throw all of your grenades right in front of him. Stay behind wall and keep cover firing on him with lancer. Doing it this way i killed him in under a minute without him ever reaching the back wall.