I do think the kanji kentei is a good exam but it is for native speakers, and the problem is that all the materials are entirely in Japanese. The first six grades from 10 (the lowest) to 5 are aimed at elementary school kids and follow the order the kids learn them at school. The next levels go up through JHS and SHS level to university and level one is for pretty serious studiers only.
We actually went to the kentei last week as my 7 year old was taking level 9 (second grade level) and my 11 year old was taking level 7 (4th grade level.)
I have been in Japan seventeen years now and can correct my younger boy’s stuff without referring to the book but the older boy’s work - fergeddubadit! It’s sort of like expecting EFL kids to be able to read American kids picture books; there’s not much writing in them but what there is is very complex.
On the other hand it is a GREAT way to learn the jukugo - the combinations that actually produce meanings and phrases. On the OTHER hand, they are aimed at the average age of the kids taking the test, so there are a lot of school type words to learn, like “school lunches” “homework”, “class rep” etc. There are a lot of really relevent to every day stuff words too.
I really would recommend you beginning from the beginning and starting at level 10 if you are going to go for studying with the kentei books, even though that covers hiragana and katakana, it does it from a native point of view.
The other way to go is to study for the Japanese Language Proficiency Test. Texts are available, they have English translations and the study order is possibly slightly more relevant to the non native student. Their vocab tends to business and university stuff which in my days of toddlers, nappies and pregnancy was totally unhelpful to me and I gave up after level 2. The JLPT is a good qualification to give to a future employer - recognised out of Japan too, as the kentei might not be…
Either way, the only way to learn kanji is to write them again and again and again and again. I like Heisig’s method of applying a story to the shape of the kanji and have taught my kids a lot of those little mental tricks (for example ani - older brother - is 兄 - a mouth 口 on legs! Which is exactly what an older brother feels like sometimes!) However you can make these tricks up for yourself, and the more kanji and kanji bits you learn, the more stories you can apply so it gets easier with time.
Finally the only way to learn kanji really really deeply is to USE them. I stopped formal study of kanji, including writing them when I had my elder son who is now nearly 12 and my kanji writing skills have almost completely withered away. I can read at about 4th grade level but writing, no. It’s a handicap with me having to deal with all the school notes etc, not to mention me having my own English school - I have to hire a secretary to do a lot of my stuff that really after 17 years I ought to be able to do on my own. So my laziness is now costing me a salary!!