No probs GRITTY_PITTY!
I think you can increase the readiness total by about 16% every 5 hours if you choose the right missions:
Terminus System - Omega
Attican Traverse - Ket'osh
Earth Systems Alliance Space - Camala
Inner Council Space - Cherk Sab
Outer Council Space - Thessia
so you could realistically have it done in a 17 hour time frame if you immediately renew the missions as they complete.
Also, if I remember correctly, the Readiness level slowly decreases if it's left alone for a period of time, but only if you are signed into the EA servers.
If you have to leave it partway through going for the trophy, sign out and you should be fine.