After Valdesi entered Beijing, he recorded all the fighting in the north. So, here's the gist of what he wrote:
On September 29th, which is the 6th day of the intercalary month in the Chinese calendar, until October 3rd, the 10th day of the intercalary month, a contingent of German soldiers led by Baron White departed from Tianjin to Jinghai County, where the Chinese forces fled south.
On October 8th, the 5th day of the intercalary month, until the 9th, the 16th day of the intercalary month, some Italian soldiers set out from Tianjin towards a place northwest of Yangcun, where any village that had killed Christians was burned down.
On October 12th, the 9th day of the intercalary month, until November 6th, the 15th day of the 9th month, the British, French, German, and Italian Allied troops set out from Beijing and Tianjin to Baoding. The Chinese army beat a hasty retreat southwest before the Allies arrived. The city of Baoding was occupied by French troops on October 14th (21st of the intercalary month). It was not until October 19th (26th of the intercalary month) that troops from other countries arrived.
After Baoding was captured, the Allied troops split into three routes back to Beijing. The British troops led by General Liche returned from Langfang Majiapu in Chengcheng County. They burned down any Boxer villages they came across. The Italian and German troops led by General Gelienni returned from Xian County, Qing County, and Huangcun, seizing the weapons of four Chinese units encountered along the way. The British, German, and Italian troops led by General Nomon returned from Yizhou and defeated a Chinese army unit at a certain location. On the way back to Tianjin, they ran into more Boxers and burned their camps.
From October 22nd (29th of the intercalary month) to October 27th (5th of the 9th month), a German unit returned from Yangcun, bypassing Xianghe County.
On October 22, 1900 (29th of the leap month), a Japanese army bypassed Baodi County via Yangcun, heading towards Hexi Wu. From October 24 (2nd of the ninth month) to November 28 (7th of the tenth month), this Japanese army returned to Yangcun after passing through Baodi County and Hexi Wu. There was also a Russian army that left Tianjin for Yangcun. Both armies ran into the Boxers and got their butts kicked.
From October 25 (3rd of the ninth month) to October 29 (7th of the ninth month), a Russian army returned by passing through Lutai and Ninghe.
On October 25 (3rd of the ninth month), a Chinese army headed out from Baoding to parts unknown, encountered the Boxers on the way, and won the battle. On October 27 (5th of the ninth month), a Russian army left Shanhaiguan for a certain place, and another Russian army also went from Shanhaiguan to another location. Both of these Russian armies clashed with many Boxers along the way and were defeated. On November 1 (10th of the ninth month), a Russian army set out from Shanhaiguan to a certain place and defeated the Boxers on the way.
From November 1 (10th of the ninth month) to the 3rd (12th of the ninth month), a German army rolled into Beijing after passing through Hexi Wu and Majiapu in Tianjin. From November 4 (13th of the ninth month) to the 6th (15th of the ninth month), a Russian army returned by passing through Yangcun and Baodi County from Tianjin. On the same day (13th of the ninth month), another Russian army went off to parts unknown from Tianjin.
From November 5 (14th of the ninth month) to the 6th (15th of the ninth month), an Austro-German coalition army went to a certain place and burned down all the villages occupied by the Boxers in that area. On November 7 (16th of the ninth month), two Japanese armies, one from Beijing and one from Tongzhou, headed to a certain county town.
From November 12 (21st of the ninth month) to December 4 (13th of the tenth month), a coalition army led by the Earl of York, consisting of German, Austrian, and Italian troops, passed through Nankou and Xuanhua and pushed a whole bunch of Chinese soldiers back into Shanxi.
On November 19, which corresponds to September 28, to November 25, which corresponds to October 4, German troops headed from Beijing towards the Great Wall and ran into the Boxers halfway, routing them in battle. On November 23, which corresponds to October 2, a German contingent returned from Tianjin, passing through Dong'an County and Wuding County. On November 29, which corresponds to October 8, German forces entered Beijing from Shanhaiguan. On December 1, which corresponds to October 10, troops moved along the banks of the Yunliang River in Tianjin towards Cangzhou, while the Chinese army retreated to Shandong.