Wow - that song has a ton of words! And as you said, there is not really a chorus that repeats over and over. This one would be a challenge for anyone and it will take some persistent practice. Storing these lyrics into long term memory will best be accomplished by spacing the learning process over a longer period of time rather than cramming it in in a short period of time.
It has long been thought by many educators that different people learn best in different ways. Some people are visual learners (learn by seeing), others are aural learners (learn by hearing/listening) while others are kinesthetic learners (learn by touching or doing).
This theory of different learning styles has been challenged in recent times and it's likely that we all learn in more than one way so it won't hurt to use all methods to help you. Perhaps you may find the one that seems to work better for you personally - but to be safe - try a combination of all. The methods detailed below employ all three of the learning styles mentioned above so you can't miss and are likely to learn in all three ways to some extent.
One thing you can start with is hand writing the lyrics on a piece of paper. This will take a little time, but the process of connecting your brain to your hand to write the words may help with memorization. This will help more if you are a kinesthetic learner but won't hurt either way.
The next exercise I will suggest has a dual purpose and accomplishes two things. Print the lyrics out so you can read them and place them in front of you. Prepare to make a recording of yourself with a recording device such as your phone, a digital recorder, or the sound recorder on your computer, or a web cam (or whatever you have available). Play the song in the background while singing it into your recorder so that your vocal is louder than the music in the background.
Concentrate on clear diction so that you can clearly understand the words. This is not a demo of your ability to perform the song. You are going to use this recording to help memorize the lyrics (words). So don't worry about being perfectly in key. Focus more on saying the right words - but sing in key to the extent you can.
The act of making the recording while reading the lyrics will advance the memorization process to some extent - just from the act of singing the lyrics. This will work for both kinesthetic and visual learners because you are reading (visual) while singing (doing). You might end up messing up on a few takes so this process will involve some repetition to get a good clean error free take. Remember - you will have the lyrics in front of you so it should not take too many takes to get them all correct.
Once you have your recording that features a clear, understandable lead vocal of you singing the song, use an ap or a program such as Audacity Audacity free download to convert your file to an MP3 for playback from any device that will play MP3 files. If you have a CD player, you can burn a CD and use the same recording as track 1, track 2, track 3, etc. for as many repeats as you can fit on your CD.
There are a number of different music player programs including i-Tunes Free i-Tunes download that will allow you to play back your recording in a loop mode that will repeat over and over. What you want to do with the CD or MP3 is play it over and over and over. Spend some time actively listening to your recording a few times, then practice singing along with your recording without looking at the lyrics. This repetition process will help tremendously if you are an aural learner (and will help some no matter what learning style you respond best to). The act of singing and listening will also help if you are a kinesthetic learner (singing).
Also, when you are driving around running errands or driving to and from work or school, you can play this over your car radio with either a CD or MP3. Play it at home when you are cooking or washing dishes or getting dressed. The more you hear it, the more of it will sink in.
Listen (aural) to your recording while reading (visual) and singing along (kinesthetic) every night right before you go to sleep. This will program the lyrics into your subconscious where it will be processed by your brain during sleep. Sleep is when the brain fortifies the link between the neurons which is why sleep is so important. Read more about how your memory is improved during sleep here: Wikipedia - Sleep and Memory
After a few days of listening while doing other tasks, listening and singing along, and listening while reading the lyrics right before sleep, try to sing as much of the song as you can from memory and make a note of the parts that give you trouble. Then you can use a free audio cutter program like the ones recommended here: Best Free Audio Trimming Programs or Audacity to cut out the part or parts you are having the most trouble with into short tracks - so you can focus strictly on those parts without having to listen to the entire song.
You can also create your own Mnemonic association devices by linking words from one verse to words from another to remember which verse comes next. For example you might use a phrase such as: "The crystallizing snow is reminiscent of a splintered crystal bell" - to help you remember the order of the four verses that start with derivations of the words used in that made up sentence.
Remember, you are not likely to convert something like this into long term memory in just a day or two. You will need to practice through repetition at various times during the day over a period of many days or even weeks before you can expect this to really sink in. But once you have it as part of long term memory, you will never forget it.
You can do it! Good luck.