Abyssinia was one of the last independent african nations just before World War 1, along with Liberia. Transvaal and Orange Free State were independent until 1910, that's pretty close. You also had the states of Darfur in western Sudan and Dervish in western Somalia, although not traditional nations, involved in the great war. There were various small states in Sudan, Somalia, Ethiopia, Chad, Libya, Niger, northern Nigeria, and present day C.A.R. also floating around resisting a bit. Morocco was independent until 1912. Zambia/Northern Rhodesia/Barotzeland was unexplored until very late and even then ruled by company rather than the crown at first. Also I believe there was a small kingdom in Senegal lingering around for a while though the name escapes me.
Source: Martin Meredith's **The Fortunes of Africa
Do you mean politically (de jure) independent, or do you include self-governing entities that are still under a theoretical coercive thumb (Egypt post-1919, South Africa even after Westminster) or an economic sort of capital-colonialism that we usually associate with the post-1957 era and Nkrumah's critiques (Liberia)? Are protectorate spaces like Morocco independent, given that they had elements of their own foreign policy?
So I think you need to define "truly independent," because by a purist's standards Ethiopia also wasn't quite independent--it had a powerful technical dependency with the French, British, and somewhat the Italians. They even sought to extend this to Japanese and US elements albeit partially because they weren't seen as dangerous as Italy, France, or Britain and would play ball. Haile Selassie I's government (and his effective control of modernization as Prince [Ras] Tafari Makonnen before) did try to balance these to straddle a middle, while seeking modern weapons and assistance in industrial growth, but colonial powers tended to shut them out--which is why the Patriots were still using Adwa-era weapons when the Italians attacked. Ethiopia was surrounded, with only the friendship of France and the port at Obock (Djibouti later) to sidestep Italy, along with the old treaties guaranteeing its territorial extent. Once Ethiopia was no longer able to leverage its position to play the powers off against one another, Menelik's 1890s policy of engagement was impossible to sustain even for the lineage of his brilliant foreign advisor Ras Makonnen. (Marcus's History of Ethiopia, while aging, is still good on this; Bahru Zewde's much more recent history is also worth consulting for it.)
[edit: missed a couple of "the"s and commas. Grammar me not good in morning ug.]