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Engineer is a pretty interesting build and it's quite good for higher difficulties. You'll be able to have a very balanced character by the end of the game. There are some good abilities and you should be able to get by with your weaponry. You'll be stuck with pistols for half of the game until you board the collector ship for the first time and gain advanced training.
The engineer's best skill is their ability to tear through enemy defenses. This is the reason for the engineer's dominance in higher difficulties. Since the major change is that the enemies have armor, shields or both, you should find it quite useful to be able to trash their protection in seconds.
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Overload can wreck shields and dish out a lot of damage against the Geth. The only reason you might want to hold back on upgrading fully is that Garrus should have this skill. If you plan on dragging him around as your soldier, then he can handle the overloads. You will need it at the second level to unlock incinerate.
Incinerate tears through armor. It's incredibly useful against krogan and just about any other enemy with a shred of armor actually. Incinerate can also just cause a lot of damage to organic life. Being able to fire off a damaging ability from cover is incredibly handy. If you don't want to spend points on this Mordin can also use it. If you plan to keep him close, then you can let this slide a bit.
AI hacking is pretty cool for most of the game, since it can turn mechs and geth against each other while you watch from cover. There's just a certain joy from sitting back and watching your enemies kill each other. AI hacking is a bit lacking on harder difficulties. You can only use it once the shields are down, which limits the time that you can use it in combat. It's also a little harder to just stop firing once you've taken their shields down. Another downside is that upgrading it only boosts the length and provides minor upgrades like giving the possessed bots shields and eventually offering an area attack at the end. It's certainly a fun ability for quickly shifting a battle, but it is going to be absolutely useless a surprising amount of the time. It also does nothing against the collectors, so keep that in mind.
Cyro Blast isn't that great. It's handy enough, but just freezing the enemies doesn't seem to do much good for a real battle. Since you will only deal with rushers occasionally, it isn't that useful. While it is fun to freeze the raging krogan or a wave of husks, you'll be better of spending the points on something else.
Finally the unique little Combat Drone is pretty cool and you'll want to upgrade it quickly. Enemies should always focus entirely on the little ball. Any enemy that you fight will stop shooting at you and focus on the ball. Throwing out a combat drone saved me several times, since it buys time to heal or move. It also lets you line up nice shots too while also doing a surprising amount of damage near the end. It can also flank enemies and it does a good job of flushing them out of cover so that your squad can gun them down easily. Best of all, it has an absurdly short recharge time. It's basically like having a fourth squad member.
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Unless you plan to do a lot of side quests, you'll probably need to decide on what path you want. A useful offensive stance is to dump your points into maxing out overload and incinerate. I personally would pick the crowd control versions at the end. Wounding a group is much better than taking out a single person. Just wound them all and pick them off with the pistol.
The support status can be a bit more fun though. By leveling up AI hacking and combat drone, you can take cover and watch your new friends destroy each other. At the worst it's a good distraction and at its best it will pick apart a mech squad. The amazing abilities of the combat drone have already been covered, but it's still great for letting you pick away at tough enemies with impunity.
Either one of these choices should be fine depending on your desired playing style. Just note that you're going to be most vulnerable against biotics users who can use barriers for superior protection. You'll either need to drag your own biotic around for support, such as Miranda's warp power. Hopefully you'll be able to upgrade the submachine gun in order to take a more direct approach to handling them though.
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On that note, weapons are pretty simple for the engineer. You'll get a good heavy pistol at the start and get a better one from Mordin during his rescue. The submachine gun should also receive plenty of upgrades during the main quest. When you go to investigate the stalled Collector ship, you will find a pile of special weapons. Engineers will lack the skills necessary to pick up the special shotgun, assault rifle, or sniper rifle. We will still be able to add free basic training to our abilities though. I grabbed an assault rifle so that I'd have an accurate weapon that had more than six shots. The shotgun could be a decent choice though for the more aggressive players.
As for your party, well that's pretty simple. Engineers will probably want at least one good soldier in their squad. Grunt should usually fit the bill, although Garrus or Mordin are also quite useful. I like to keep a biotic around too, so in my game I kept Jack nearby. I'd drop the shields with an SMG and she'd send them flying away.
This should cover the best methods for making an engineer in Mass Effect 2. I hope these engineer strategies work out for you.