The 19-year-old from Bolton in Lancashire added a one under par 71 to her opening 70 to sit at three under par after two rounds at Golf de Batalha on the Portuguese Atlantic island.
The 2010 British Ladies Amateur champion now has a strong chance of becoming the first amateur to win on the two-year old Ladies European Tour Access Series.
The last amateur to win on the top flight Ladies European Tour was South Korean Amy Yang at the 2006 ANZ Ladies Masters in Australia.
Tidy was not particularly pleased with her round, which contained two bogeys, at the fifth and the seventh holes, but she recovered with birdies on three of the four par fives: the ninth, 10th and 13th.
“I started with a shaky round, scrambling a par on the first hole and it took me some time to get in the groove of things,” said the England international.
“The birdies on the ninth and tenth gave me a respite and the one on the ninth was the turning point. I must say, I'm happy with the 71 today, even if I had birdie chances on the 12th, 16th and 18th. The putts lipped the hole on all of them. The course was wet and slower than yesterday, but in great shape.”
Far from being nervous, she was relishing the opportunity to contend in a professional tournament before heading to the Ladies European Tour’s Qualifying School in January.
“I would not say it is strange for me to lead a pro tournament because I have played with the pros before, twice in Murcia, in Turkey and also at the Women’s British Open,” she said.
“Tomorrow I'll try to make a lot of pars but everybody knows me: I am an aggressive player and I'll go for my chances if I see the opportunity.
“I'm working on a few things but I can still improve tomorrow in terms of strategy on certain holes.”
Second placed Spanish professional Mariana Macias Capuzzi was satisfied with her round of 74 despite taking a double bogey seven on the par five ninth hole.
She said: “I'm playing well and enjoy the course very much. I'm not a long hitter but I'm sharp with my irons and short game and hit a lot of greens. I could have had a better score if I had putted a little better, but I'm feeling well with my game and I have a chance tomorrow.”
A number of other players were still within touching distance of the title including French amateur Alexandra Vilatte and Dutch professional Marieke Nivard placed six shots off the lead on three over par.
Ireland’s Tara Delaney and Holland’s Marjet Van der Graaff were a shot further back, seven off the pace. Nivard and Van der Graaff both need a top-two finish if they are to secure one of two cards available for the 2012 Ladies European Tour.