Pick one opening played by top players whose games you can use as a model. Keep playing it over and over until you get good at it. Regard your losses as new lessons to learn.
Hypermodern openings for black

Dutch fights for the centre from move 1. That is not hypermodern.
OP asked for hypermodern openings.
As far as I know ,Dutch , Bird , English and Sicilian were never considered hypermodern openings.
The English Defense is indeed a hypermodern opening as it follows all rules of the hypermodern opening:
1) Neither center pawn advances two squares early
2) It allows the opposing player to create the big center
3) At least one bishop is fianchettoed
Openings that fit this category are (fianchettoed B in parenthesis):
King's Indian Defense(DSB), Nimzo-Indian Defense(LSB), Queen's Indian Defense(LSB), Modern Benoni(DSB), Benko Gambit(DSB), Modern Defense(DSB), Pirc Defense(DSB), English Defense(LSB), English Opening(LSB - Certain Lines, not all lines), Reti(LSB - Sometimes both), Larsen's Opening(DSB), etc.
I'm sure there are a couple I missed and don't claim it to be 100% exhaustive, but now you have some idea what is defined as a Hypermodern Opening.

I don't mind playing a gambit, I do understand that material is not everything. But I'm afraid I'm not that good with tactics (I'm better with positional advantages) and might not make the most of the Benko. Nevertheless, I think I'll give it a try, as I have seem some nice games in it by my teammates. I'm also going to take a look at some other recommendations from here, thank you!

Can someone recommend me an opening for black against 1.d4 where you fianchetto the DSB and play in a hypermodern manner? I've already tried playing the KID, the Grunfeld, the Modern and now the Benoni, but I'm not having a real good time with them.
Thanks in advance!
english defence

Play 3...c5 and you enter Pterodactyl territory, maximally leveraging the power of your sniper bishop. Try it! It works. Now if white plays e4 to occupy the center, you can play Bxc3+, capturing the knight and weakening his queenside. Followups are f5 and if exf5 Bxf5 as well as Qa5.

if you want to use your dark squared bishop to the best of its ability, then play the grunfeld
its often a very strong, active piece and is key to breaking through whites center
but you could also play the mar del plata if you like those types of positions
ive done alot of analysis on the grunfeld and kings indian so if you want some i can give you some

Old benoni
the old benoni will either transpose into the normal benoni OR go into a worse version for black

Old benoni
the old benoni will either transpose into the normal benoni OR go into a worse version for black
I was looking through Old Benoni lines recently and discovered that in 99% of Old Benoni games, e6 just doesn’t get played. It makes a lot of sense, considering that d6 is a weak pawn in the Benoni, but in the Old Benoni, there’s no need to take on d5 because there’s no pawn on c4 stopping a queenside push.
In the Benko the pawn is not lost
It's like to lose one penny and gain a pound.