Tanks, originally designed to be a source of mobile firepower able to negate the power of the machine gun, quickly turned into a psychological weapon for the allies through the entirety of the war, and it took both strong resolve and hardened veterans to counter the weapon.

As you mention, soldiers unfamiliar with tanks described them as "beasts," notably in The Great War: A Combat History of the First World War by Peter Hart, where one green German soldier panics about a "crocodile" in their lines. After the first use of the tanks at the Somme, the rumors quickly spread through the German army, causing considerable morale depletion. While soldiers who did survive long enough began to grow accustomed to the sight of such terrifying technology, it was no less disheartening when it was made specifically to counter the small arms that were available to most soldiers and would likely create a sense of hopelessness. I would argue that the tank was almost as much a psychological weapon in its early years of design as the flamethrower and poison gas.

So, what was the German response to tanks? Well, their preliminary ideology was to make use of weapons already available to them, ranging from concentrated artillery on approaching tanks, concentrated machine gun fire on thinner, weaker parts of the hull, using the makeshift "reverse bullet," to even using the improvised "geballte ladung" hand grenade Ludendorff, an opponent of tank usage, insisted even in his postwar memoir that all that was needed to counter tanks were "solid nerves, discipline, and pluck." To a certain extent, this was true. Even in the latter half of the war, German ideology for fighting tanks required soldiers able to perform under high stress situations. These chosen men would perform actions such as lugging light guns through mud as a mobile, close-range response to tank assaults, or attempting to kill crew by targeting viewports or weak points with the rifle fire, later K-bullets, and by the end of the war, the Tank Gewehr. Quick-thinking troops such as one German Lieutenant (unnamed in Russel Freedman's The War to End All Wars: World War I) describe taking advantage of blindspots on allied tanks to climb above them before throwing grenades inside.

As for some obscure responses to tank warfare, there are two I'm aware of. Thanks to the curiosity and recklessness of Major Bernhard Reddemann, the Germans were also able to discover the unique effectiveness of the flamethrower, which, when used against tanks, would consume the limited oxygen supply in the enclosed vehicle and could light the fuel reserves on fire. Another option was to simply ignore them entirely. Tanks were of limited use on their own, as seen at the Battle of Cambrai, and German troops recognized the validity of hiding while the tank passed by before reestablishing their posts to fire upon the vulnerable infantry that would come next.

Finally, a tactic that saw minimal use but would prove to be seen often in the next major war would be that of tank-on-tank. The two examples I'm aware of are that of are at the villages of Villers-Bretonneux and Cachy. Both involved the A7V on the German side and the British on the other. Villers-Bretonneux would see the Germans suffer heavier damage, with one vehicle abandoned, while Cachy saw two Mark A Whippets taken out of action. Both were results of the victor having their vehicles armed with more cannon.