You are probably using the wrong equipment to get a good amplified sound from your acoustic guitar.
1) You can't get a good sound by running an acoustic guitar through an amp designed for an electric guitar. Amps designed for electric guitar are designed to color the sound and add distortion (by very subtle amounts or in the extreme) and they do not reproduce the full frequency response of the acoustic sound of the instrument.
On the other hand, there are special amps designed for amplifying acoustic guitar; for example, the Fishman Loudbox series. They are designed to "purely" amplify the sound without imparting any artificial coloring, distortion, compression, etc. If you are serious about getting a good sound from your acoustic guitar, you should invest in a dedicated acoustic guitar amplifier. They can be quite expensive, because they produce much higher audio fidelity than your average electric guitar amplifier.
2) Performers who want to amplify an acoustic guitar for stage use, if they do not purchase a dedicated acoustic guitar amplifier, always use a dedicated external acoustic guitar preamplifier which is used in conjunction with a direct box, so that the guitar's signal can be sent not to a stage amplifier but directly to the hall's mixing console, thence to go straight to the hall's stereo speakers/PA system.
3) Most, but not all, guitar multi-effects units have effects and reverbs and compressors, etc. which are designed to bring out the best sound in an electric guitar, not an acoustic guitar. Your Boss GT10 is not advertised as being useful for acoustic guitar. You can create some interesting experimental sound effects by running an acoustic guitar signal into such a multi-effect unit, but you won't get a good, natural-sounding acoustic guitar sound from one of these. They are simply not designed for that.
Go to a music store and take your acoustic guitar with you. Ask to play your guitar through various acoustic guitar preamplifiers or multi-effects units specifically designed for acoustic guitar (there are a few on the market). Let your ears guide you.