To get the achievement, you need to beat the whole game without a single weapon zooid. You might be thinking "Boy that's a bit of a slippery slope there, bub" and you would be correct, BUT there is one species that shall be the basis of your trek: The Advena.

The Advena species has a potent and powerful utility zooid that spews jets of poison of which debuffs whatever enemy zooid floats through it. That shall be the crux of this strategy for one reason alone: it's reliability. Sure the other species' utility zooids might entice you like the Buginis' miner or the Cra'thran's sizzler, but the other species' utility zooids either do no damage or are otherwise unreliable. However, you shall require an adapted zooid; of which you will not expect (or did if you already know)

The adapted zooid shall be: The Grappler

A shock, I know. I have tried many combinations of adapted zooids and other species to get this achievement. None of them worked, except this one for reasons I'm not too sure of. One observation that I noted was the grappler damaging the zooids it came into contact with almost rivaling that of the Advena's harpoons but with a MUCH longer range.

Getting the optimal level at start takes some time so don't be afraid to try it out. If you fail, then try again. Do not be discouraged by failure at the beginning as it takes time to get used to the setup.

I also HIGHLY advise changing the keybinds of your sipho to shift key for your dash as that actually makes SOME sense. Leaving this tangent, however, the optimal level for this build shall be The Azure Depths (Saenus Beefuorus home level). While the big pincers on them may look scary and their bubble pushers will try to push you away, YOU have an advantage in both cases. Just use your poison as you back away from the ones with pincers, and use your grapplers to latch onto those who try to push you away.

This will guarantee an excellent start to your journey.

Depending on your starting level if you did not perish you may need to assess the boss before engaging. This may help you if you are stuck.

Saenus Beefuorus Boss 1 (Guardian of the Depths):
Use the strategy detailed in the previous exhibit to deal with this one. There are some other things to note: It will always return to the center of the arena, if it has it's claws then it will try to push you periodically, and if it lost it's claws it will push you constantly.

Buginis Boss 1 (The Queen's Guard):
Try to pull the smaller one to you first so you can use your poison to render it deceased. To ensure a swift kill stay in it's weak point (not the front).
The larger one will require more tact and skill. If you have the nutrients for it, then going in for the kill can be viable, but if not you shoult try to pull it's side to you so you may shred it at your leisure.

Advena Boss 1 (Venomous Pit):
This is the easiest to deal with as it has the most weak spots to take advantage of and ample cover to hide behind. First pull the poison side to you through one of the gaps and then lay into it. The boss should go down relatively easily.

Cra'Thran Boss 1 (Cra'Thanos' Clench):
This is the most difficult first boss without weapon zooids. I have but two suggestions as to how to deal with it. Stay away from it's leeches and sizzlers and utilize the poison to whittle it down, and one any openings are available, use the grapplers to sever zooid connections.

I cannot tell you how to play your playthrough of Sipho beyond the first boss as I feel that will rob you of your discovery and enjoyment. However, I can grant some last word advice as to some challenges:

If you are facing a whole horde of small siphos use the poison as a form of crowd control.

When dealing with the Cra'Thran species, aim for the main sipho with your grappler and kill them quickly.

You do not need a particularly large sipho to be deadly, just large enough to have a variety of tools.

If you can, pairing the grappler with the agonizer can yield more damage than before. Attaching the agonizer to a structure zooid with a poison will not yield more overall damage.

Do not underestimate the power of the poison debuff as you can kill a sipho with just three well aimed squirts.

You can use the grapplers to maneuver larger siphos through tighter spaces than they can swim through.

This is where I will post updates and edits if I make them. Have fun with this strategy and build.