Thanks for your replies, guys.
After seeing some of this videos I got some inspiration and decided to try something different before removing the spring. This, my friends, is the story of How My R4 got it's Click-And-Spring Back.
1· Open the cartridge.
2· Go to the memory slot. There you'll find a metal flap to the left. Blend it up so you can access the spring mechanism.
3· If you now try to reinsert the SD card, you'll notice a black device going up and down. Don't try much harder, it still doesn't work.
4· You'll also find a metallic pin. Ok, that's the part that's failing. On normal functioning, that needle should move to the left and to the right whenever you push a SD card in and out, allowing it to spring to the outside or keeping it in (alternatively, left and right, left and right). Your SD card doesn't spring-and-click anymore because this pin has got out of its rail.
5· Take a small screwdriver/toothpick/whatever small enough and put the needle in its place. Use your SD card pushing it in to see how the needle flips to the left and to the right alternatively as it should.
6· Put the metallic flap we removed in step 2 into place and hold it lightly against the memory slot. Now push again your SD card in and rejoice seeing how it clicks and is held into the slot perfectly. Now, here comes the bad news, the flap has lost its flexibility and can't keep the needle in its place, so once you release your finger, the SD card springs out like before (only this time you're unaware and the card flies through the room or at least that's what happened to me).
7· Cut a small piece of fine cardboard the size of the memory slot and use tape to fix it in place.
8· Mount the cartridge and good as new!