The most annoying aspect of this otherwise great game is that certain fights are deliberately hard to find. Searching for them requires considerable backtracking, which can kill the pacing. This is a list of these hidden Verses, locations only, including Alfheim Portals. I kept this brief for convenience and tried to be reasonably spoiler-free.
When my directions are particularly vague use the Verse numbers as your general guideline. For example Chapter 2 Verse 8 should be sought out after finishing the non-hidden Verse 7.
Many players would suggest that you shouldn't even worry about these hidden Verses until you've replayed the game, making my avoiding spoilers a pointless distraction. There's some merit to that approach, but since many of these Verses (particularly the Alfheim Portals) also serve as training for more complex techniques, you might find the game more enjoyable if you try to be a Verse completionist from the start.
Verse 3 Alfheim 1
After repairing statue, go back down the hole.
After fight at fountain, backtrack to elevator.
Verse 5 Alfheim 2
Jump the car, find its source.
Verse 6 Alfheim 3
Small walkway up above, before courtyard.
Verse 8 Alfheim 4
Backtrack as far as you can go.
Verse 2 Alfheim 5
Go up the steps and destroy the garbage can. The portal will appear underneath a building nearby, next to two benches.
Verse 5 Alfheim 6
When you get to the two statues, go in the opposite direction and look for the balcony. There's barrels underneath it.
Fight in the lava tunnels. (This isn't actually hidden, but I found it easy to accidentally skip on replays.)
Verse 10 Alfheim 7
On a small island in the water.
Verse 11 Alfheim 8
After restoring the bridge, go back into the cave.
Verse 3 Alfheim 9
Back to the start.
Verse 8 Alfheim 10
Get almost to the top, then drop back down to the ground. (You can look down first to see if the glowing portal is activated.)
Verse 10 Alfheim 11
After exiting tower, take lower path.
Backtrack to where Verse 11 was.
Verse 4 Alfheim 12
Before opening second door, backtrack to first door.
Verse 2 Alfheim 13
Break the big door.
Verse 7 Alfheim 14
From the floating wreckage, fly to the glowing light.
Go up ramp, look for angel statues and destroy them.
Verse 11 Alfheim 15
Before entering tunnel, backtrack all the way to where Verse 8 was.
Verse 3 Alfheim 16
Turn to white platform first.
Verse 9 Alfheim 17
From red portal, backtrack.
After red portal, fly to the white platform.
Verse 3 & Verse 4 Alfheim 18
Kick open the door, then head all the way back to the start. After beating Verse 3 the gate for 4 will appear.
Verse 6 & Verse 7 Alfheim 19
This is slightly complicated so I'll go into detail. Jump into the enormous engine. During Verse 6 you need to use Witch Time to get all the way to the back of the tube so you can then access 7. Afterwards any projectile weapon can get you back out.
At this point you know what to do with statues, right?
Verse 9 Alfheim 20
Before taking the elevator, backtrack to the start and fly over the chasm.
Explore the room with the giant statue.
Investigate the large platforms until they are dead.
Verse 5 Alfheim 21
When you get to the neck, backtrack.