ACROSS
2 - Win over the damsels finally in a deuce battle (6) - {S}{EDUCE*}
7 - Girl and you are in this city (4) - {}{U} (Addendum {G}IF{U} - See comments)
9 - Race track has an opening for Batman after Michael (4) - {O}{VAL}
10 - Hit my mom's gray pet monkey (5,8) - PYGMY MARMOSET*
12 - Retirement money (7) - PENSION [CD]
13 - Flier's charge put on board (7) - AIRFARE [CD]
15 - African country has limited small leading industries (4) -
17 - Mess up this and that around the campus initially (5) - {BOT{C}H}
18 - Soundly pull in what's left (4) - R??? (Addendum - REST (~wrest) See comments)
19 - One toad is disturbed by an insect (7) - ODONATE*
21 - Water source I regularly conceal in the pudding ingredient (7) - {TAP}{I}{O}{C}{A}
23 - Documents may require this to be official in nature (13) - CERTIFICATION [CD]
27 - Cut off the play place for men only (4) - STAG
28 - Checks out a point very well (4) - {E}{YES}
29 - Girl will first learn to ride out in an aircraft (6) - {G}{L}{IDER*}
DOWN
1 - Honest small little devil of the French (6) - {S}{IMP}{LE}
2 - Note the second guest doing mischief regardless of the Democratic leader (10) - {S}{UGGESTION
3 - This may be imposed on imported goods (4) - DUTY [CD]
4 - Baby bear film in this country (4) - {CUB}{A}
5 - Plays with kids' stuff (4) - TOYS [DD]
6 - Picks up the coat in an adventure site (8) - ?A?T?R?? (Addendum - {C}{APTURES*} See comments)
8 - Broke one limb of an Indian plant (5) - {BIML*}{I}
11 - Girl inside has some kind of plant sugar (7) - {M{ANN}OSE*}
13 - Monk in charge follows to rebuild the caste (7) - {ASCET*}{IC}
14 - The garden helper (10) - FERTILISER [CD]
16 - Sailor will heartlessly order to quit (8) - {AB}{DIC
20 - Not thin (5) - THICK [CD]
22 - Pass on the snooker sign in English in the capital of Yugoslavia (6) - {CON}{V}{E}{Y}
24 - Encouraged a bit of an angry display (4) - RAGE [T]
25 - Favourite line of God is set back outside (4) - {IDO<-}{L} ?
26 - Dry air is flowing at the tip of the desert (4) - {ARI*}{D}