I was able to beat the Cthulhu campaign this weekend. For those who are throwing their androids against the wall, I hope that this helps.
1/ Solo with Jenny. Simple enough, she has a great ability and it makes it simpler to control.
2/ You should be able to get the 7 Elder signs in the Museum without any doom tokens. If you have 1, don`t worry about it.
3/ When in the pacific, focus on the Relic items until getting the 3 gems. Having the artifact which allows you to replace 3 green dice is also going to be extremely handy. Use Excess investigation dice to get the 30 necessary tokens needed to find Ryleth.
4/ VERY IMPORTANT, is to take your time. I found that this scenario is kind of like Conflict at the Carrock for Lord of the Rings. It looks really scary until you learn how to beat it. I was using Jenny slowly to accumulate tons of Trophies. I went to the hospital many times to ensure she was healthy.
5/ By the time the doom token was 10, I was spending lots of time in the ship stockpiling clues and spells. I faced Ryleth with about 7 clues, 2 lock spells, and 1 relic to replace 3 green dice, all in addition to Jenny`s red and yellow dice. Needless to say, the boss fight was pretty easy.