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On the lower difficulties the campaign doesn't feel right on terms of how hard the orks are, but on the max difficulty it's too far the other-way.

Are there any tactics for the first two levels, the morale loss from the objective tokens is brutal yet rushing them is not possible when the orks have such numeric supremacy?

I'd managed to beat the first level with the modded space marines being dropped straight into the second objective. But the spaceport level is even worse, open terrain and too many buggies to rush the objective in the open.
This question / problem has been solved by NathanHimage
For the first mission my strategy is as follows:

Rush the bridge objective with a predator. Set up your predators to the left of the bridge, on the near side of the "river". Bring up the space marines behind them. The Orks will give too much respect to the predator firepower, and keep their forces out of range and out of the firing arcs. You can move the predators around a space or two every turn to get line of sight on Orks that think they are hidden, and then drop back to the preferred position. This should allow you to snipe the occasional Buggy.

There are two ways this setup can get you into trouble. The first way is for Orks to pop up out of the hills to the left where your line of sight is unreliable. If this is just Boyz, then this won't be a major problem. Your predators are basically immune to Boyz and they don't co-ordinate these attacks well enough to overwhelm your Space Marines. You might have to withdraw a Marine unit if it takes too many casualties, and you might lose one, but this is manageable. More dangerous are the Buggy attacks. These can sometimes kill a Predator, and if you lose 2 Predators it's probably game over. However, they don't usually do this very often. If a Buggy is sneaking up on you from this side, you can often assassinate it with a Thunderhawk. The rockets + battlecannon attack will usually kill a Buggy. You have to be careful not to get shot up when retreating the Thunderhawk however. You can move it down to Height 1 when moving in and retreating to minimise overwatch.

The second and more dangerous possibility tends to be the Orks sneaking up to the Bridge and contesting this objective. Their Buggies are quite good at doing this, and they will probably set you back too far with losing the objective and killing Predators. The reason they manage this is that the combination of Bridge, small Forest, and small Supply Dump completely mess up line of sight. Therefore my first actions with the Thunderhawk and Whirlwinds are to destroy this Forest and then destroy the Supply Dump. If you do this at the right time, you can even ambush the Buggies with your predators and kill 2 or 3 in one turn. Eventually, you'll be able to clear the Buggies from the right side of the map, and the remaining Boyz are not much threat.

Once the Buggies to the right are neutralised, you can start advancing a Predator along the road. The Orks continue to respect the range of the Predator and will retreat around it. Combining Predator attacks and Whirlwind bombardments you should be able to clear a path to the objective if necessary, though in practice I find that you will have killed enough Boyz and Buggies for your morale to be superior and you can just wait out the win. If things got really bad, you'd probably have sufficient superiority on the right side to do a Thunderhawk drop and claim the objective.
I just tested a new approach for the second mission. It is strategically risky but seemed effective. Immediately delete Commissar, Mordian Command, and 1xChimera. Buy a second Heavy Weapons squad. This lowers your morale by over 100, so reduces the time you have for missions, but none of the units you've removed ever do anything apart from pad your morale total.

Again, we are going to take advantage of the fact that the Orks respect the Heavy Weapons too much. They'll be remaining at range 29 and their range is 20, so we're going to be pretty safe unless a stray Buggy decides to attack. Set up with 6 Heavies in your remaining Chimeras. In the first turn, move the chimeras to their maximum speed and unload the heavies. Move up the 4 remaining heavies and the Thudd Guns. If the Bombards have any targets, open fire, otherwise clear out the crates to the right of the spaceport. The Orks will be out of range of your Heavies, so there's no threat this turn.

Turn 2, move the rearmost heavies up and have the Chimera go back and pick them up. Your remaining Heavies can advance 1 square and shoot twice if possible, otherwise move them 2 squares. You can also move 4 squares to keep pushing the Orks back quicker, but this reduces your firepower. You should keep the heavies advancing at the same rate as one another, otherwise the ones further back will be out of range---your target should be to shoot twice with most Heavies each turn, at least for the first few turns.

Prioritise killing the Buggies since these can move forwards faster and potentially kill a Chimera. You don't have much morale to play with using this strategy. Once you've killed the buggies and pushed the Ork Boyz far enough back, you can zip a Chimera up to the middle objective. I did this on Turn 8. By Turn 10 my morale was higher than the Orks, and I eventually won at turn 14 with zero losses (indeed, not a single guardsman killed). I took a few shots to a Chimera but that was all.

Main threat in this mission was the crates to the right allowing some Boyz and a Buggy to get within range.
I can't manage on any setting higher than easy. I've almost managed the first engagement on the next highest, but there are too many buggies and my Predators get taken out.
I'll try the advice here if I find the time. At this stage I'm playing mostly for those 'epic' cutscenes..
I find that playing on the highest difficulty will come down to a very narrow point spread, so get used to that high anxiety play. On both missions you need to prioritize conserving your higher scoring units while sniping the buggies and bikes with artillery.

For the first mission I dropped the Space Marines on the bridge with the Thunderhawk on turn 1, and with their remaining movement entrenched on the near side of the bridge, creating a fatal funnel, and cover on the flanks (check your field of fire with one of the icons to make sure you're in a good spot). I moved two Predators up behind the marines on the bridge for support, and one to the left near the forest to cover the northern approach. Once I had that first objective I could take the enemy as they came. I used the Thunderhawk to harass northern / western infantry, and to snipe at bikes when I could - fly in, shoot em up, fly out.

The second mission was more touch and go. What worked for me is to lead with your lasgun infantry and chimeras in one line, with the heavy weapon infantry out of range of ork boyz. Inch this force up while retaining at least one fire action - two is better, but will require you to make a mad dash for the first objective towards the end. Since your force is primarily infantry, you'll want to prioritize killing ork boyz with your infantry and chimeras - use the bombards on the bikes and buggies. Do not discount the thudd guns. They are slow and relatively weak, but shoot at whatever is in range when it comes in to range - if nothing is in range, move them up aggressively. As soon as you feel comfortable, move a chimera or the rhino to grab the objective and keep the enemy from contesting it.

After these missions, when the real game opens up, I shuffled units around quite a bit. I removed the thudd guns and one unit of chimeras from the first battalion and replaced them with the Leman Russ and Basilisks - this is my primary battalion and have been using it for most of my current game. The Tallarn battalion will be pretty weak, so don't use it until you can afford to beef it up later in the campaign. Whichever army you use, do not forget to get AA batteries! Try to conserve your tanks as best you can and get them experienced. Once the gargants start rolling out in the counter attack, you'll want something that can reliably get through the shields and armor.

Have fun!
Thanks managed the beat the spaceport with 15 morale left!