I like to build poses from the ground up. Here's how my mental checklist usually goes:

1. Feet
2. Legs (always double checking the position of the knees/hips)
3. Core
4. Low back
5. Chest
6. Upper back
7. Neck/shoulders
8. Arms
9. Head

The same thing goes for muscle engagement. 

If you engage your muscles in warrior 2, you will find that you can hold it for longer. You will also find that your body opens to new possibilities of movements, and your asana practice slowly grows more advanced! 

In Warrior 2 all of us pay LOTS of attention to our front quadricep. Sometimes we pay so much attention to this muscle that we don't engage anything else.

Always remember, as you tire, find different muscles groups to recruit to help you!

Here's my Warrior 2 muscle engagement checklist:

1. Energetically squeeze the feet together on the mat to activate the inner thighs. 
2. Pull the low belly in and up. 
3. Knit the front ribs into the body to help with core engagement. 
4. Tuck the tailbone to lengthen the low spine and help with core engagement. 
5. Squeeze the glutes, especially the back leg