While assessing and opening notes on 4 patients in 30 minutes would be ideal....I think that your preceptor might be rushing you a bit.
When you do your initial assessment, go ahead and "eyeball" it, like your preceptor suggested. That doesnt mean you cut corners, but if you peek in on your patient and see that he/she is lucid, talking on the phone, walking to the bathroom etc...you know that his/her resp are even and unlabored, they are ambulatory, a & o x 3.
When I worked days, I would peek in on all my patients to make sure they were alive and breathing, introduce myself, then start pulling meds (we have a one hour window at our hospital for meds). While giving meds in the room, I would go ahead and assess lung sounds, bowl sounds, pulses, etc....it saved alot of time doing it that way.
On good days, I would be able to assess my patients, pass 9AM meds, and open my notes on 6 patients within 1.5-2 hours.
Everyone opens their notes differently. I never put "rec'd patient alert and oriented x 3, bed rails up x 2" because thats already covered in one part of our chart (its sort of like a check off thing on our notes). Avoid double charting and you will save yourself alot of time. My opening note is usually something like "Dx: cellulitis to LLE. Pt is a 54 yo male, resting quietly, 0 c/o pain, 0 s/s of distress. IVF infusing to LH at 100cc/hour via pump. LLE elevated on pillow. V/s stable. Will continue to monitor for acute changes." The entire physical assessment is already covered in the check off part of my notes, so I dont need to double chart about lung sounds or bowel sounds etc....
I know that everyone has a different way of doing things, and chances are there is going to be someone out there that will criticize the way I do it...but this is what works for me.