Achievement description does not say when exactly it will be "big enough" explosion to get achievement but this guide will help you focus what you really need to do in order to finally get that achievement
The easiest way to get that achievement is to invest as much as possible points to explosive damage tag type.

First - If you have bomber badge and it is upgraded to maximum - you get +5 explosive tag damage type on start








Bomber badge

As characters select the ones which have explosive tag type weapons and abilities(e.g Tank, Huntress and Swat)

To have most of the time to get that achievement pick endless game mode(I didn't try if it is possible to get it within 20 minutes of standard game mode)

For items the most important one to obtain is the Ultra Instinct one.









Once you achieve at least 30 damage type tag - all other damage tag types will go to the one which has achieved at least 30 damage type tag thanks to that item. You don't need to have 30 points once you take the item - so if you have rerolls unlocked you can try your luck to get it in early game and then get to 30 points of explosive type tag as soon as possible so other abilities which are granting other damage type will be automatically transferred to explosive one









If you will be lucky enough to get The Bomb item it's great as you get +5 explosive damage type as bonus
In fact when I got the achievement didn't have it but it will speed up the process.

Some comments say ability area also is useful to invest in but in my opinion I think explosive damage tag type does the job to get that achievement and the Ultra Instinct item is essential one there to get it.
Additionaly you can get different type of gems before getting ultra instinct to get as many points in other areas as possible to transfer it later on by Ultra Instinct. It's more luck based as there is no guarantee you will get that item during the run so once you get chance to get it - you probably want to go with it instead of selecting something else as it might not appear again during the runs until next time.

Generally speaking It's in fact the easiest way to get it but might be time consuming due to RNG in order to get the Ultra Instrinct item which will allow you to get more explosive type damage tag points - as for me without that item my maximum of that tag including the bomb item was at 42 and it was not enough to get achievement.

I finally got it when I had like 54 of explosive damage tag type so my assumption is that you need to have at least 50 points of explosive damage to get big explosion enough to trigger that achievement(sadly no way to test and check that theory).

That's it. I hope it will help you to get it the easy way :)