Yes, you have to have a slot2 expansion cart (Ewin 2in1 or EZ 3in1) for the browser to use for extra memory. Then you have to do one of the following:
1. Use the GBA Loader to patch the slot2 expansion cart (trick the browser into thinking it's a memory cart). Run GBA Loader 1.6 and press L+R then A to patch the expansion cart. The NDS should soft reset back to TTMenu where you can then run the browser (if it doesn't reset back to the menu, you'll need to turn off the NDS manually and immediately turn it back on -- the patch will remain on the slot2 expansion cart -- then run the browser).
2. Use the latest version of YSMenu (a homebrew menu for the TTDS) which automatically patches the expansion cart when you run the browser.
It should be mentioned that there are several homebrew browsers that don't require extra memory expansion. They come in two general flavors, and they are typically much faster than the Opera browser. Some of them render only text and (small) images and are therefore fast but don't support all HTML features. Others rely on a PC to render the HTML and then send the resulting image over the WiFi to the NDS, and therefore do full HTML but require a server running on a PC to operate.
Can't you use a Slot2 linker (let's say G6Lite) as memory expansion ?
I saw there was a TriForce patch for Opera Browser and G6Lite(M3). I tried it (DSTT+G6Lite) but it fails loading (freeze when I launch the browser)
You can use the G6 Lite, yes, but I believe you need the G6-specific patch, as the G6 is not the same as the M3. If it fails upon loading, my guess is that it isn't the slot-2 device you're using, as you should be able to at least get to the "please insert slot-2 RAM pack" message without anything in slot-2.