Actually it takes about 4-5 months if everything goes smoothly.
Without spending trophies you get 4 fights a day, multiply that by 30 and you have 120 per month.
For random encounters with other glads on average idd say you should look at 4 fights per month as a minimum also so that's another 120 per month.
That makes 240 per month in total, multiple that by 4 and you have 960 fights so you will "only" need 4 months and a week.
In terms of training points coz I feel like it, 4 from fights, 10 from tavern quests so that's 14 training points per day and wow now that I look at it Nate that amount sucks.
So multiply it by 30 you get 420. Multiply that by 4 and you have 1680. This is without adding the couple of training points you also get from lvling up.
If I remember correctly it takes about 1800 training points to max your skills out if you get really lucky. Lets add a 400 training points to that because it's almost impossible to have that luck. Hence it takes 5-6 months to max out a glad on skills with normal luck