Yep, we got our game played and I decided to make this battle report with more pictures and less text.
I began the game with rolls like these: 1,1,2,1, which meant that we got seize ground with 3 objectives, my opponent got to place the first one, the deployment was pitched battle and that he got the first turn.
The necrons deployed thusly (one squad of warriors and a monolith was left in reserve with the monolith deep striking):

So now that I got something to actually think about, I think it's time for some tactical assessment. So the necrons are not obviously using the monoliths to shield them, which means I have to prepare for some portal shenanigans. The monolith and nightbrinder took central positions which allowed them to react to whatever would happen. They are both very slow models so one has to be careful with their positions. This meant that I couldn't get to the squishy warriors without having a monster in my face. I have no idea why the scarabs were deployed so far back because he had the iniative. I would also have to put a great deal of my army to my right because that black objective simply had to be assaulted. You can just see the red objective behind the middle ruin while the green one is behind that white cardboard ruin. The destroyers were hovering the ruins behind the monolith.

Then I deployed very widely, trying to use those ruins to gain cover to my best ability. My demolisher faced the monolith as it had the best chances of destroying it. I did a mistake by deploying it so close because the particle whip would reach it after the monolith moved. Since concentrated fire achieves something I also put two lascannon squads to the left of the demolisher with clear line of sight to the monolith.
My left spearhead was the two chimeras. They contained the grenade launcher command squad and my psyker and the other was empty. It's pretty obvious were they were going. I chose them to took on the destroyers as they had lots of str6 shots. In the middle I put my blobbed autocannon squads, the third lascannon squad and my
CCS. The synergy which these units give each other was just superb: re-rolls to morale, BiDs and general protection against any units the enemy has to throw against them.
My right spearhead consisted of the flamer command squad and the melta veterans in their chimeras. They were supported by my sentinel, infiltrated harker and my leman russ. Note that the leman russ battle tank has a clear sight to the necron lord's squad. All in all I was ready to take on every threat. Oh yeah, I left Marbo, airborne assaulting storm troopers and rough riders in reserve.
My series of bad rolling took a surprising twist as I seized the iniative after proclaiming it loudly.Yeah!
Imperial Guard turn 1: 
So my might trudged forward. All of my units took either defensive positions behind ruins or each other or positions with clear sight to the enemy. Harker's devils were the only infantry units to move forward and this only to get the grenade launcher ready to lob.
My company commanders ordered the lascannon squads to let their projectiles loose! The results were _very_ destructive. First lascannon immobilised the monolith. The next one destroyed a weapon. Then the demolisher added to the fire and also penetrated the metal monster, damaging another gauss flux arc weapon. I did not even need those re-rolls and I got 3 hits and all 3 of them penetrated. That's how you're supposed to take the iniative. The blob squad found out that the star god's necrodermis wasn't that strong and took two wounds off the beast. The right half of my army could only manage trivial casualties with the battle cannon drifting off the table and other weapons generally failing to wound. One necron warrior stayed dead after we'll be back rolls. A good turn all in all!
Necron turn 1: 
The monolith couldn't move anymore so the middle force slogged forwards. The scarabs relied on their 2+ cover save and turboed in some ruins, threatening my blob. All these units ran a bit.
The warrior squad near the black objective took some potshots at my meltavet chimera and shook it.

The necrons on his right had better luck and the only one that was facing the side armour of the lead chimera penetrated 3 times after futile cover saves and exploded the vehicle. I was lucky for it to be the empty chimera. At this point I also realised that spidey was on the table too. The monolith could not even glance my demolisher though it hit.
Imperial Guard turn 2:

My flamer vets went ballsy and defied the C'tan's powers. I saw a great opportunity to get rid of the fast and durable scarabs and put my templates on them. Their courage proved to be useful as the scarab cloud disappeared from sight. Meanwhile my rough riders and Marbo appeared. Marbo came forth from the destroyers' shadows. My rough riders did not want assault the nightbrinder yet as it could survive (I did not remember the etheric tempest rule at this point).

My shaken meltachimera took a position to attack the nightbringer next turn. My demolisher backed away from the monolith and got ready to blast those warriors. The rest of my army either remained in place or shuffled around a bit to get better shots.

All of my shooting (demolition charge, pieplates, harker, chimeras) dropped 9 warriors in total. The lord's resurrection orb really was worth its points. All of the destroyers would have died but I advised my friend to go to ground and it paid off as one destroyer remained, although pinned. By the way, can a pinned unit go through the monoportal to get re-rolls to
wbb rolls? I couldn't wound the nightbringer at all with my blob this turn.

These guys have reaped impressive amounts of high-value targets, especially deathwing terminators. These valiant knights have however had bad luck against 'crons with gaze of flame and lightning arc... thankfully now the enemy only has gaze of flame.
Necron turn 2: 
Anyone could have guessed the fate of my perhaps foolhardy command squad, needless to say, they got eaten. And their chimera got shaken by gauss weapons.

The rules question did not matter this turn as all 3 destroyers got back up on their own and so opened the gate for this necron squad which only lost 1 model after all. Not much happened this turn because the monolith was out of range, the destroyers were pinned and the tomb spyder couldn't reach Marbo.
Imperial Guard turn 3:

I committed my last reserves and decided to use them to help me get that necron objective. They deep struck on target. They stormtroopers themselves only killed one necron but Harker's squad, leman russ and sentinel pounded them to the point they had enough and phased out on double sixes.

Other units moved forward again except for the shaken chimera which got closer to Harker, ready to pick them up. And so to the main objective of this shooting phase... The C'tan was felled with the first bring it down shots. Apparently a C'tan's only weakness is autocannon rounds (my opponent failed all 5 invulnerable saves he got to roll). My demolisher shot at the lord's squad and dropped one while on the left flank my psyker and his grenade launching friends killed all four destroyers again. This turn there was some seriously bad rolling by my opponent. To add insult to injury, Marbo charged the tomb spyder and wounded it once while the construct couldn't land a blow.

Now I know what the rule "fearless" means.

End of the top of turn 3. It looked very bad for the necrons with only Lord attached to a warrior squad, immobilised monolith and badly beaten spyder on the table. However, there was still a surprise in the darkness of a tomb world.
Necron turn 3: 
Monolith arrived and scattered in a ruin. It took some time to find out what actually happened. I just couldn't say that the ground level's wall was impassable so roll for mishap and instead we counted the monolith as deep striking onto the ruin. The model couldn't fit on the small floor so we just left it on the ground (please remember that when you look at the following pictures. The monolith often changes place.). Skimmers can only be placed on ruins if they can be physically placed on it but here the monolith deep struck. It also couldn't move vertically because the model can only move 6" which means after two floors there's not any movement left for horizontal movement. Remember that impassable wall on the ground level. It's like the game glitched right there. What's your opinion on this?

The reserved warriors came out too but had to disembark from the other monolith and so they moved towards the objective.

As did the other warriors.

Marbo my man survives yet another turn in close combat and hit&runs away.
Imperial Guard turn 4: 
My right spearhead moved on as planned.

The rest of my army closed in on the newly arrived warriors.

My shooting was however very dismal with both of the leman russ blasts scattering away.

Which is why Marbo challenged the spyder again, this time poisoning it to death.
Necron turn 4: Both warrior squads moved closer to the objectives and did nothing with their shooting. The derp struck monolith immobilised the leman russ battle tank.
Imperial Guard turn 5

Okay, time for the final mop-up. Harker's newly acquired chimera parked on the black objective and the melta vets sped towards the necrons and disembarked. The rough riders prepared for a long charge against the teleported necrons. Marbo and my primaris psyker also came to ensure their destruction.

The diminished warrior squad wiped the meltaveterans who charged them. They actually weren't allowed to do charge in the first place.

The necron forces were about to phase out.
Necron turn 5: 
The last necrons on the table after
WBBs. This was not quite enough as they phased out, granting me a wipeout.

Endgame.

I also had all 3 objectives in my firm grasp as if phase out wasn't enough.
So, it was a fun game although I had superior luck to the necron player's abysmal luck. Seizing the iniative, penetrating the monolith 3 times with 3 shots and annihilating the C'tan really made this game somehow one-sided. I would have wanted a bit more challenging game with my finished army but for the most part we had good time so it doesn't really matter. I simply have to challenge the necrons again!