I have 1882 survival trial points according to ranking.
The server started on Aug 1st. The ranking counted toward Jan 8, so that's 1932 possible.
In other words, I have missed a total of 50 nodes over the course of 4 month.
Pretty sure that's mostly in the first 2 weeks, where I'm missing 1-4 nodes daily, and ALL in the first 2 month.

So yes, it is very possible. And I have always been a ftp, so there were quite a few ptw ahead of me which I frequently encountered for 11 and/or 12th node during the first 2 month(after which they no longer showed up, not sure why)

The idea is to use a sustain team (heal/shield whatever) to get pass the first 9 flawlessly (or, before you can sweep as you can't clear 12, at least first 6 and then take minimal damage with absolutely no death up to 9).
After that, 10 you should be able to beat fair and square, on 11 you need to use your best judgement, you should try and make a team that is excellent at either countering or killing a single unit off the enemy team here (unless you can beat it easily w/o significant damage). Same idea on 12, except here you really can throw all your spare ninja at him JUST TO KILL ONE CHAR. Breaking his chase chain by burning off your off team while entering with a full, thou possibly lightly damaged, team will give you significant advantage.
Remember to observe the fights while fighting with off team, restart if needed.
You are looking for that lucky fight where: enemy doesn't proc a chase off normal attack (unless it's guaranteed, in which case you should use something with clones to absorb it), your normal attack DOES proc a chain on them (unless it's impossible due to clone/earth main etc). Also observe their chase sequence to see which is the best to kill. What the relative init is so you can consider either try to interrupt their mystery OR delay your own so it doesn't disappear etc.
First time is hardest because you can't sweep, ergo your team might be lightly damaged (anything above a total of 10% health between all char is a failure on your part even w/o sweep thou), after that it will get easier.
Also, if you have any kind of healer, remember that when enemy is down to one or two char, you CAN stall the fight so you can heal up more. This is especially true if the enemy is a healer or tank like hinata, kabuto etc who can't really deal any damage to you. Stop using offensive mystery and start slowly heal up, it will help toward the next fight.