
I don't read shoujo, but this one always gets recommended. :D
http://www.mangago.zone/read-manga/anatolia_story/

the female lead hardly lose to the guy whenever they argue http://www.mangago.zone/read-manga/takane_to_hana/

Mentally strong and extremely independent female lead - http://www.mangago.zone/read-manga/akagami_no_shirayukihime/
Both mentally and physically strong female lead - http://www.mangago.zone/read-manga/akatsuki_no_yona/
Both mentally and physically strong female lead, also this manga is hilarious (no romance) - http://www.mangago.zone/read-manga/oresama_teacher/
I don't even like shoujo that much, but I extremely love these three! ALL RECOMMENDED!

http://www.mangago.zone/read-manga/skip_beat/
my favorite one :)

Tokyo crazy paradise.-who needs the male lead when the female takes all the action?
W juliet
Grand Sun - physically and mentally strong female lead.
Basara-rival of anatolia in my opinion. One of the best!
Fushigi yuugi Genbu Kaiden - strong female lead Mentally and emotionally
Hana ni arashi - physically and mentally strong female lead.
From far away/kanata kara - Mentally and emotionally strong female lead.
NG life - Mentally strong female leads. One of the best!
Sakura Rhythm- i guess the female lead is mentally strong.
Your My Girlfriend. - Mentally strong female lead.
Tomodachi no Hanashi. - strong female leads i guess?
Dengeki Daisy - Mentally and emotionally strong female lead.
Last game
Kono koi wo wasurenai (chapter 3)
Hyakuen Renbo - Mentally strong Female lead
Beast Master
Immortal Rain - physically and mentally strong female lead.

http://www.mangago.zone/read-manga/beast_master/
http://www.mangago.zone/read-manga/tokyo_crazy_paradise/
http://www.mangago.zone/read-manga/keishichou_tokuhanka_007/
http://www.mangago.zone/read-manga/dengeki_daisy/
http://www.mangago.zone/read-manga/hana_ni_arashi/
http://www.mangago.zone/read-manga/he_s_dedicated_to_roses/
http://www.mangago.zone/read-manga/hana_no_kishi/
http://www.mangago.zone/read-manga/the_one/
http://www.mangago.zone/read-manga/sp_x_baby/
Shoujo with strong female lead (physically or mentally or both) thanks!