Depends on the quest. Promotion class quests often has a second page. (When you open up the quest from the quest tracker item in your inventory, press the right arrow.) If you're using MTOOL, you should see this item in your "key items" list. You cannot open up this item while any member of your party is pregnant, pregnant but not yet showing, or exhausted.
For B-Class promotion, I cannot remember. For A-Class, IIRC, you need to kill 20 SSR rating enemies, which your MC need to be the only to deliver the killing blow - these SSRs are only available as the Floor 3 (bottom floor) bosses of the 6 guild managed dungeons.
Also ,what do you mean you cannot read because of mtool? Mtool is supposed to translate it... Can you screenshot what you're seeing?