As someone who took 準一級 and 一級 last year when I was in Japan (153点 and 100点 respectively; I was really hoping I could pass 1.5 but oh well, I’m happy I was able to get exactly 50% on level 1 given 1.5 months of rigorous study haha), I have to say that once you get to higher levels, knowing how to write the kanji becomes a matter of course (once you understand that most kanji are just building blocks of one another). Currently I am in university so while I am still studying some parts of the kanken (notably 四字熟語 writing, general reading, 熟字訓, and 諺), my time available to put into kanken study is reduced; after all, Japanese isn’t just about the hard to read kanji!
The difficulty in those tests rather becomes, as another replier has mentioned, the ability to recall, accurately read, and write extremely esoteric kanji and kanji compounds.
Personally, the most difficult part of 1.5 was a section where you have to come up with a given kanji within the joyo set given an example sentence and a hiragana bank. I was able to get I believe full marks for the reading and I believe 29/30 (don’t quote me on that though haha) on the standard writing sections. 四字熟語 is also a good source of points.
For level 1, aside from simply not knowing some words, I got absolutely annihilated with a section where you are given the meaning of a 熟語 and a hiragana word bank and you have to write out the word. From what I have been told that section leads to 0/10 for many new test takers.
Also, while the difficulty curve is relatively linear for levels 10 to 2.5-2 ish, I need to warn you that the jump from 1.5 to 1 is about an order of magnitude, as the amount of kanji and words related to said kanji one needs to know essentially doubles from all other levels. At this point, you should be able to write all joyo kanji with no issues, including the infamous ones like 鬱.
Some of the more “common” level 1 compounds/kanji can be seen in literature, and if you go back to older works (think around the Meiji era), you’d be surprised to find quite a large amount of these kanji being used (my guess being that the education system put more focus on Classical Chinese at that time).
Hope this helps.
So you basically wrote out the characters as they came up in WK? Thanks for sharing! Keep them coming 
I was exactly like you and tried to brute force my way to study it like I was studying English or some Romance language. I did RTK1 (Jalup’s Kanji Kingdom) then used ASK’s Try series – the whole series – as a dictation anki deck. Over my time studying through the JLPT levels, I turned literally all of the sentences from N5-N1 into dictation cards. Front: audio, back: sentence. I wrote sentences out using kanji and everything when prompted by the audio.
