The other solution says what to do, but doesn't give a good way to accomplish this.
First though, to start a mission, you need to hit the ball into the URU hole 3 times to drop the barrier, then hit it into the yellow sink hole behind that.
To make this easier, you need to master the Lightning Strike combo.
Look at the table by holding X. See the upper right mini ramp behind the upper right flipper? That's the YMIR ramp.( 1 letter of YMIR lights up every time you hit the ball through it) If you hit the ball there using the upper left flipper and then immediately pull back on the launch Stick ( right Stick) it will push the ball right through the destroyer ramp ( lights up 1 letter of ARMOR every time you hit it up that ramp)
These 2 ramps are the hardest to hit and this makes it a little easier. Now to make it even easier to hit, hit the ball up the Loki Ramp ( the green one, lights up 1 letter of Serpent every time you hit it up there) Once the ball goes up the ramp and starts down, pull back on the launch stick, the right stick. This will drop the ball just above the upper left flipper making hitting the YMIR and Destroyer much easier.
Practice it til you are good and you will have a much easier time completing these missions. Now on to the missions.
This mission requires you to defeat Loki. Hitting the yellow ramps will take 1 point of health from Loki, hitting the blue ramps takes 1 point of health from Thor. Each has 7 hit points. However I usually hit Loki's green ramp then hit the Lightning strike combo. This will take off 1 point from Thor, but take 2 points from Loki. Since this is the easiest ramp for me to hit, that's what I always do. Simply hit any yellow ramp a total of 7 times will accomplish this.
If you look at the dot matrix, you'll see that the counter is counting up from 50%. You want to make it go down to 0. Hitting either of the yellow ramps on the left will lower the percentage about 10%. Hitting the bumpers above the volcano will lower it about 2% per bumper hit. Depending on which flipper the ball is on determines what you should shoot for. I usually try getting it to the left bumper and hitting it around the far right ramp into the bumpers. Hopefully it will bounce off these lots of times in a quick succession and end the mission quick. Although it might just hit them few times and bounce out. Keep hitting either the yellow ramps or the bumpers to complete the mission.
You must hit the lit lanes to attack Ymir. Unfortunately many times you don't have a good shot at them and for this mission you can't hit Lokis ramp to do the lightning Strike combo so I'd suggest almost any time you have the ball on the left side, keep hitting Lokis ramp because this will bring Thors health up a little. There are only 2 lanes lit at any time and they change every 8 seconds or so if you don't have a good shot at one, wait til the lanes change and be mindful of Thors health. If it's getting low, hit Lokis ramp a few times to bring it up.
The Destroyer in Asgard
Here's where the Lightning Strike Combo really comes in handy. You must hit 3 ramps in order to hit the Destroyer and you have 60 seconds to hit all 3. If not, Thor looses 1 point of health. The 3 ramps are the destroyer ramp, Ymirs mini ramp, and the little U-ramp to the left. You must hit them in order. If you hit the URU hole, this will drop the ball right above the upper right flipper for a shot at the destroyer ramp. I only seem to hit this about 25% of the time. However if I hit the Loki ramp I can easily do a lightning strike combo and hit it easy. Then do the combo again to hit the Ymir ramp. In less than 10 seconds I have 2 of the 3 ramps usually. Then I just need to hit the remaining ramp before the 60 seconds is up.
If you miss the Loki ramp or the combo after the first destroyer ramp shot, if you hit the URU hole, this will deposit the ball right above the top left flipper for an easy shot at the Ymir ramp.
You need to hit these 3 ramps 3 times to complete this mission.
Ymir Rages Again
You need to hit 2 ramps 3 times to complete this mission. However there is ice blocking the ramps. So you must first hit the ball into either holes under the volcano to light the ball on fire. Then hit the ice twice each before sending the ball through the ramps. You must do this 3 times to complete the mission. This is the hardest mission at least for me because many times hitting the ball into the ice sometimes results in the ball bouncing into either out lanes or right down the middle.