How to get started with battery replacement in a bluetooth speaker?
There are two battery specifications you'll need to match:


Nominal voltage
Max current draw


The nominal voltage is the average voltage a cell has when charged. For a single cell Li-Ion battery it's around 3.7V but we don't know how the battery pack is made up. If it's two cells in parallel or some other kind of configuration. The max current draw is how much current the battery would be expected to produce under full load.

Usually, when you dismount the unit this information is printed on the battery pack. If it's not you'll have to look for a replacement battery (contact their support for the model number) and just use that. 

I didn't say you had to match the capacity (stock capacity is 3600mAh) since you can get a smaller or larger capacity and the unit will still run just either shorter or longer than expected. As long as the battery can physically fit in the unit you'll be fine but you have to match the voltage. The max current rating can be higher, but not lower. 

As for tools, it looks like you'll need some small screwdrivers and a pry tool. Any precision toolkit should serve you well. Just be careful when inserting the pry tool so you don't cut any waterproofing seals. Though, don't expect it to be 'weatherproof' when you reassemble.

You shouldn't need an antistatic band but it's good to have one if you can get it. You will likely need to desolder the battery connections to the main PCB and resolder the replacement battery to the main PCB (Printed Circuit Board) or it could be connected via a JST connection. You won't know unless you get the full schematic or dismount.