Just beat this today without too much trouble. Here are a few tips if you are having a hard time beating these missions.
1. Don't worry about your ratings. You only need to beat the missions.
2. Stick with your assault rifle for the most part. I only used the shotgun against the riot enemies with the shields, krogans and centurions when they are close enough.
3. Use cover as much as possible to avoid unnecessary damage. The enemies will take you down fast if you are out in the open too long. Also, make use of jumping between covers when available.
4. If you haven't done so already, upgrade your assault rifle and shotgun to the max. This will help greatly to take down enemies quicker.
Last Boss tips (Ogre Mech)
As soon as you enter to door, stay relatively close to the first pillar, but do not use it as cover. You want to basically shield yourself from the ogre using the pillar as it is attacking you.
Wait for the ogre to attack first. This is important. If you start attacking the ogre right off the bat, you will more than likely get killed. It has three different attacks it uses - red ball, yellow beam, and its turret. These are all very easy to dodge as long as you are moving around close to the first pillar.
After it uses one of its attacks, strafe to the right so that the ogre is in range and unload on it with your assault rifle or shotgun. Do this only once as your weapon will overheats. After it recharges, take out the two weaker mechs coming towards you down the hallway. Once your weapon recharges, wait for the ogre to attack again, rinse and repeat.
I was able to beat the ogre first try in a few minutes using this method.
Another final tips if you are still struggling - always be aware of the weaker mech enemies coming down the hallway. If you start taking a lot of damage, take them out first if they get too close.