Blackberries are typically bitter particularly when not growing in ideal conditions. I would recommend starting with improving your soil by mulching heavily. Also, make sure they stay well watered while the fruit is ripening up. And don't run your berries through a blender. Blenders tear up the berries and release bitter compounds. Freeze them, thaw them out, crush them, then press them. Let your wine age for at least a year to give it a chance to mellow out. I wouldn't suggest making a dry wine with blackberries unless you have primo sweet berries. Somewhere between a table and dessert wine would probably be better in order to have the sweetness balance the bitterness.

Are you crushing, or including the seeds during primary fermentation? You may want to strain the juice first. Seeds can definitely cause bitterness. Same with stems, as they both can contain tannin. Some people want those tannins because they add character. However, keep in mind that the reason most anything tastes 'tart' is because it has very little-to-no sugar. You might try using a different yeast. A 'strong' yeast can be resistant to 'death by alcohol'. Get a yeast that quits at a lower alcohol level and/or maybe use less sugar in your recipe. Another trick may be to use that fruit that makes anything taste sweet... 'Miracle Berries.' Let us know if these things work.

7 1b yeast lavlin yeast are suppose to mellow out the malic acid (which is the main acid in black berries lavlin is supposed to be GMO free.

I agree with not using a blender, and freezing the berries is good

Did you age it a year

Have you tried adding honey? or more of it? Sometimes it can take more than you think. Grapes are naturally super sweet so they wouldn't require much sweetening, but blackberries would. Hope your batch turns out this year!

An old post, yes, but there's clearly a misunderstanding of tastes that we (should have) been taught back in grade school. Bitterness is not tartness.

The OP asked about tartness. This is the perception of acidity, specifically citrate, malate, and, in grapes, tartrate. Yes, a lack of sweetness can cause an imbalance in the wine and increase the perception of crisp/acidic/tart. Acids are mouth-watering. Think: sour patch kids candy or Granny Smith apple.

Bitterness, on the other hand, is different. This is what comes from the polyphenols (aka: tannis) in the seeds, stems, and, to a lesser extent, the skins. Smaller chains of these are perceived as bitter (taste) and are in the seed and stems, and longer chains are astringent/dry/grippy (mouthfeel) and are found in the skins. Crushed seeds increase the surface area of the seeds and subsequently the amount of extracted short-chain tannins, making the wine more bitter. Tannins are mouth-drying. Think: over extracted tea.

I would not hesitate to ferment whole fruit and would advise against straining or pressing the fruit first. The goal is to extract all the color and softer tannins from the skins possible and to treat this more like a red wine than a white. Mixing the fermenting must a few times a day is essential. Press only when its dry or very close to dry.

If you want the acidity to be reduced, while not adding sugar after alcoholic fermentation is complete to achieve a better "balance" in your wine, look into doing a malolactic fermentation. There are several ML bacteria strains that don't impart the huge buttery flavor associated with oaked Chardonnay. As was mentioned, aging will help soften the astringency, too.