Quests are tiered in different levels. On their most general level, quests are broken into G Rank, High Rank, and Low Rank, in descending order. From there they are further broken down into stars, starting at 1* and going up.
The different ranks of the quest will determine difficulty, obviously, but how so, you’re wondering? The most obvious difference between Low and High Rank, and High and G Rank, is the health of the boss class monsters. Not only for difficulty purposes, but to compensate for more powerful equipment, monsters in higher ranks have higher health. They will also hit for much more damage, mandating that you have the respective armor. And, especially in G Rank, boss class monsters will have new attack patterns and movements to trip you up. Their movement might also be sped up, just to make life more difficult. Within a specific rank, low star quests will be easier than high star quests. High star quests will increase difficulty by introducing more aggressive species of monsters.
To move up a star, you must complete specific Key Quests . No, you don’t have to 100% the entire list of 1* quests (except in the solo campaign where they’re just tutorial quests) but it’s not a bad idea to do so for the practice and rewards. After you have completed the key quests, an Urgent Quest will pop up. This is
going to feature an objective much more difficult than the star itself, and is actually one star above the quest tier you are currently at. It is meant to test your skills. Complete the urgent quest, and you will unlock the next star of quests (which the urgent quest will then join as part of that list for you to farm if you need to).