Yesterday I played around with the grinding the Mother sword and got it to +17 so far.
I'm following the Japanese guide linked in the previous post. To be honest I mostly skimmed it, but if I got the details correctly, this is the way that uses the least Lambda grinders etc.
■Preparing fodder (NT☆12 weapons, should have Embrace before being used)
①+26
②+30,+15
③+30, +24
■Upgrading ☆13 weapon
④Upgrading to +10 (Use fodder ①
⑤Upgrading to +20 (Use fodder ②
⑥Upgrading to +30 (Use fodder ③
⑦Upgrade to +32~35 using the same name weapons
I feel like this is pretty easy to follow, doesn't take that much money and you only use 5 lambda grinders for steps 4-6.